|
2016
|
|
Nov 11:
|
International Colloquium of Algebra, Number Theory, Cryptography and Information Security
|
ANCI, Taza
|
Invited Keynote
on Recent Progress in Determining p-Class Field Towers, Taza, Morocco
|
|
Sep 08:
|
Sensational Discovery of the First Three-Stage Tower
|
F3∞K/K
|
of 3-Class Fields over a Cyclic Cubic Field K with Conductor 28791=9*7*457
|
|
Sep 07:
|
3-Principalization Type and Second 3-Class Group
|
Gal(F32K/K)
|
of all Cyclic Cubic Fields K with 3-Class Group (3,3) and Conductor c < 100000
|
|
Aug 20:
|
Long desired discovery of a Second 5-Class Group of Elevated Coclass
|
cc(G52M) ≥ 3
|
for the Cyclic Quartic 5-Mirror Field M=Q((ζ-ζ-1)d1/2) with d = 8689
|
|
Aug 09:
|
5-Principalization Type and Second 5-Class Group
|
Gal(F52M/M)
|
of all Cyclic Quartic 5-Mirror Fields M=Q((ζ-ζ-1)d1/2), d < 10000, with 5-Class Group (5,5)
|
|
Jul 25:
|
2nd International Conference on Groups and Algebras
|
ICGA, Suzhou
|
Invited Lecture
on p-Capitulation over Number Fields with p-Class Rank Two, Suzhou, China
|
|
Jun 28:
|
18th Postgraduate Group Theory Conference
|
Imperial College, London
|
Presentation Three-Stage Towers of 5-Class Fields, London, UK
|
|
Jun 25:
|
Fork Topology, Contestants, and Shafarevich Covers
|
cov(G,K)
|
of metabelian 3-groups G32K with Kernel Type F and Coclass 6 over quadratic fields K
|
|
Jun 15:
|
Annihilator Ideals of Two-Generated Metabelian p-Groups
|
Article
|
establishing the general templates S,W,Y and verifying the specializations L,X,Z,R,T,V
|
|
Jun 07:
|
Precise Artin Patterns (kernels and targets of Artin transfers)
|
AP=(TKT,TTT)
|
of all 24476 complex quadratic fields with discriminant -107 < d, by far most extensive computation up to now
|
|
May 30:
|
Recent Progress in Determining p-Class Field Towers
|
Invited Lecture
|
for the International Colloquium on Algebra, Number Theory, Cryptography and Information Security in Taza, Morocco, 2016
|
|
Apr 29:
|
Sensational first realization of the 5-Sylow subgroup of the symmetric group of degree 25 as
|
2nd 5-class group
|
Occurrence for the real quadratic field with discriminant d = 27186289
|
|
Apr 07:
|
Sensational discovery of the first 5-CLASS TOWER OF EXACT LENGTH 3
|
Priority Claim
|
Occurrence for the real quadratic fields with discriminants d = 3812377 and 19621905
|
|
Mar 16:
|
Precise Artin Patterns (kernels and targets of Artin transfers)
|
AP=(TKT,TTT)
|
of all 34631 real quadratic fields with discriminant d < 108, by far most extensive computation up to now
|
|
Mar 13:
|
Recent Progress in Determining p-Class Field Towers
|
Abstract
|
for the International Colloquium on Algebra, Number Theory, Cryptography and Information Security in Taza, Morocco, 2016
|
|
Feb 28:
|
On class groups of imaginary quadratic fields
|
Math. Rev. 3404031
|
of a paper by A. Wiles, in J. London Math. Soc.
|
|
Feb 18:
|
Annual Report 2015 for the Austrian Science Fund (FWF)
|
Report
|
Stand-alone research project P 26008-N25
|
|
2015
|
|
Nov 24:
|
Artin transfer patterns on descendant trees of finite p-groups
|
Adv. Pure Math.
|
6 (2016), no. 1, Special Issue on Group Theory Research
|
|
Nov 12:
|
Grunwald-Wang theorem, an effective version
|
Math. Rev. 3368167
|
on a paper by S. Wang, in Sci. China Math.
|
|
Oct 18:
|
Induced homomorphism (quotient group)
|
Article
|
induced homomorphism, characteristic subgroups, GI-automorphisms, functorial properties
|
|
Sep 30:
|
New number fields with known p-class tower
|
Tatra Mountains Math. Publ.
|
64 (2015), 21-57
|
|
Aug 31:
|
22nd Czech and Slovak International Conference on Number Theory (CSICNT) 2015, Liptovsky Jan, Slovakia
|
Presentation
|
New number fields with known p-class tower
|
|
Jul 21:
|
1st International Conference on Groups and Algebras (ICGA) 2015, Shanghai, China
|
Presentation
|
Invited Lecture on Periodic sequences of p-class tower groups
|
|
Jul 09:
|
29th Journées Arithmétiques (JA) 2015, Debrecen, Hungary
|
Presentation
|
Index-p abelianization data of p-class tower groups
|
|
May 18:
|
École de Recherche CIMPA UNESCO 2015
|
Oujda, Morocco
|
La théorie algorithmique des nombres (lectures and exercises)
|
|
Mar 25:
|
Higher Newton polygons and integral bases
|
Math. Rev. 3276340
|
of a paper by J. Guàrdia, J. Montes and E. Nart, in J. Number Theory
|
|
Mar 08:
|
Descendants of <64,75> as second 2-class groups of biquadratic Dirichlet fields
|
Q((-1)1/2,d1/2)
|
Special instances of the cases A and D by A. Azizi and M. Taous
|
|
Feb 25:
|
Annual Report 2014 for the Austrian Science Fund (FWF)
|
Report
|
Stand-alone research project P 26008-N25
|
|
Feb 18:
|
Index-p abelianization data of p-class tower groups
|
Adv. Pure Math.
|
Special Issue on Number Theory and Cryptography
|
|
Jan 30:
|
Coclass of Gal(k2(2)|k) for some fields k = Q((p1p2q)1/2,(-1)1/2) with 2-class group of type (2,2,2)
|
Report
|
on a paper by A. Azizi, A. Zekhnini, and M. Taous, in Journal of Algebra and its Applications
|
|
Jan 27:
|
Periodic bifurcations in descendant trees of finite p-groups
|
Adv. Pure Math.
|
Special Issue on Group Theory
|
|
2014
|
|
Dec 10:
|
The group Gal(k3(2)|k) for k = Q((-3)1/2,d1/2) of type (3,3)
|
IJNT
|
in cooperation with M. Talbi, A. Derhem, Mm. Talbi and A. Azizi
|
|
Dec 08:
|
Principalization of 2-class groups of type (2,2,2) of biquadratic fields
Q((p1p2q)1/2,(-1)1/2)
|
World Scientific
|
Int. J. Number Theory 11 (2015), no. 4, 1177-1215, DOI 10.1142/S1793042115500645,
in cooperation with A. Azizi, A. Zekhnini and M. Taous.
|
|
Nov 13:
|
Quadratic p-ring spaces for counting dihedral fields
|
World Scientific
|
Int. J. Number Theory 10 (2014), no. 8, 2205 - 2242, DOI 10.1142/S1793042114500754.
|
|
Oct 23:
|
Principalization algorithm via class group structure
|
CEDRAM
|
J. Théor. Nombres Bordeaux 26 (2014), no. 2, 415 - 464.
|
|
Oct 07:
|
Signed fundamental domains for totally real number fields
|
Math. Rev. 3198753
|
of a paper by F. Diaz y Diaz and E. Friedman, in Proc. London Math. Soc.
|
|
Sep 19:
|
Endowing descendant trees T(R), R = <81,2> and <81,5>, with structure
|
by implementation of the
|
Artin transfers for p-groups G having G/G' = (p2,p2) or (p3,p)
|
|
Sep 18:
|
Entering uncharted waters by construction of descendant trees T(R) with
|
roots R = <81,2>, <81,5>,
|
consisting of 3-groups G with abelianization G/G' = (9,9) or (27,3)
|
|
Sep 16:
|
Completely new perspective of the population of coclass trees T2(R) with
|
roots R = <243,6>, <243,8>,
|
based on computations of IPADs by M. R. Bush and TKTs by D. C. Mayer
|
|
Aug 27:
|
Structural interpretation of composite Artin transfers
|
Article
|
Wreath product of symmetric groups Sm and Sn with respect to {1,…,n}
|
|
Jul 31:
|
p-group generation algorithm
|
Article
|
p-covering group, nucleus, allowable subgroups, orbits, step sizes
|
|
Jul 19:
|
Complex quadratic fields of type (3,3,3)
|
Preprint
|
Infinite 3-class tower, transfer kernels and targets, and second 3-class group
|
|
Jul 12:
|
On the Hilbert 2-class field tower of some abelian 2-extensions of Q
|
Math. Rev. 3165518
|
of a paper by A. Azizi and A. Mouhib, in Czechoslovak Math. J.
|
|
Jul 05:
|
Principalization in algebraic number theory
|
Article
|
Artin reciprocity law, commutative Artin diagram, and Galois cohomology
|
|
Jun 16:
|
Artin transfers and structured descendant trees
|
Article
|
Inheritance from quotients, stabilization criteria, and pattern recognition
|
|
May 28:
|
Strategy of pattern recognition via Artin transfers
|
Preprint
|
Arithmetical applications of: commutative Artin diagram, inheritance from quotients
|
|
May 21:
|
Descendant trees of finite p-groups
|
Article
|
Nuclear rank, multifurcation, coclass graphs, parametrized pc-presentations
|
|
Apr 12:
|
Principalization of 2-class groups of type (2,2,2) of biquadratic fields
|
k = Q((-1)1/2,d1/2), d = p1p2q
|
in cooperation with A. Azizi, A. Zekhnini, and M. Taous, in IJNT
|
|
Mar 27:
|
Annual Report 2013 for the Austrian Science Fund (FWF)
|
Report
|
Stand-alone research project P 26008-N25
|
|
Feb 28:
|
A new computational approach to ideal theory in number fields
|
Math. Rev. 3105943
|
of a paper by J. Guàrdia, J. Montes, and E. Nart, in Found. Comput. Math.
|
|
Jan 31:
|
On the strongly ambiguous classes of k|Q(i) where k = Q((2p1p2)1/2,i)
|
Review
|
of a paper by A. Azizi, A. Zekhnini, and M. Taous, in Asian-European Journal of Mathematics
|
|
2013
|
|
Dec 18:
|
West Coast Number Theory 2013, Asilomar, Monterey, California
|
Presentation
|
Class towers and capitulation over quadratic fields
|
|
Nov 17:
|
Classification into principal factorization types of pure quintic fields
|
Q(D1/5)
|
by means of metacyclic class number relations and relative norms of fundamental units
|
|
Nov 06:
|
Using Pari/GP and Magma for the classification of pure cubic fields
|
Q(D1/3)
|
into principal factorization types, according to Barrucand / Cohn
|
|
Nov 03:
|
Using ANUPQ and Magma for descendant generation of <729,9…12>
|
of type (9,3)
|
as an important supplement to the descendant trees of <729,13…21>
|
|
Oct 25:
|
Units of pure quartic fields Q(p1/4) with p ≡ 7 (mod 16)
|
Math. Rev. 3059109
|
of a paper by A. Aguilar-Zavoznik and M. Pineda-Ruelas, in Far East J. Math. Sci.
|
|
Oct 20:
|
Determining the index of relative units of pure quartic fields
|
Q(D1/4)
|
by means of calculating the relative norms of a fundamental system of units
|
|
Oct 07:
|
Using ANUPQ and Magma for descendant generation of <243,3>
|
of type (3,3)
|
to get the complete overview of transfer kernel types in section F
|
|
Sep 23:
|
ÖMG and DMV Congress 2013, Innsbruck, Austria
|
Presentation
|
Abstract
,
3-class field towers of exact length 3
|
|
Sep 01:
|
Official Start of our International Research Project
|
FWF: P 26008-N25
|
Towers of p-Class Fields over Algebraic Number Fields
|
|
Aug 30:
|
French translation of the CIMPA - UNESCO Lectures "CIMPA 2015 Oujda"
|
Resumé
|
Théorie des Nombres Algorithmique et Applications en Cryptographie
|
|
Aug 25:
|
Complete Proposal for the CIMPA - UNESCO Course "CIMPA 2015 Oujda"
|
Summary
|
Computational Number Theory and its Applications in Cryptography
|
|
Aug 22:
|
Inspired by some presentations at "Groups St Andrews 2013":
|
Preprint
|
Complete Normal Lattice of metabelian p-groups G, G/G' ≅ (p,p), k(G) = 0
|
|
Aug 19:
|
Generalization of our lecture at "Groups Saint Andrews 2013"
|
Preprint
|
PC-Presentations for infinite periodic sequences of 3-groups G, G/G' ≅ (9,3)
|
|
Aug 03:
|
Groups St. Andrews 2013, Fife, Scotland
|
Presentation
|
Abstract
,
Finite 3-groups as viewed from class field theory
|
|
Jul 05:
|
Celebrating the Thirtieth Anniversary of my Ph. D. Promotion
|
July 5th, 1983
|
Periodicity and Structure of Non-Metabelian Relators, Zassenhaus Filtration
|
|
Jul 03:
|
Non-metabelian finite 3-groups G with transfer kernel type κ(G) in
|
Section E, cc(G) = 3
|
First Non-Metabelian Parametrized PC-Presentations
|
|
Jul 02:
|
First step to find all finite 3-groups G with transfer kernel type κ(G) in
|
Section E, cc(G) = 2
|
New Metabelian Parametrized PC-Presentations
|
|
Jun 17:
|
The distribution of second p-class groups on coclass graphs
|
CEDRAM
|
J. Théor. Nombres Bordeaux 25 (2013), no. 2, 401 - 456.
|
|
Jun 09:
|
Tough computation of second layer pTKTs κ2 over complex quadratic fields
|
of type (3,9), such as
|
K = Q((-64671)1/2) of pTKT A.20, κ = (444;4), having a sensational κ2 = (333;2)
|
|
May 28:
|
Discovery of further 3-towers having three stages over number fields
|
of type (3,9), such as
|
K = Q((-320968)1/2) of pTKT C.4 in its 1st excited state, by D. C. Mayer
|
|
May 05:
|
First evidence of 3-class field towers having three stages over number fields
|
of type (3,9),
|
for example K = Q((-42567)1/2) of pTKT C.4, κ = (112;2), by D. C. Mayer
|
|
Apr 13:
|
Criteria for sextic Pólya fields of type K = Q(ζ,D1/3),
|
ζ = exp(2πi/3),
|
based on investigations by Amandine Leriche (Amiens & Lille)
|
|
Apr 05:
|
2nd 3-class groups G32(K) of cyclic cubic fields K
|
of type (3,9)
|
and their connection with 2nd 3-Genus Groups g32(K)
|
|
Mar 15:
|
Statistics of 2nd 3-class groups G32(K) of cyclic cubic fields K
|
of type (3,3)
|
Frequency of Abelian, Coclass 1, and Coclass 2 Groups
|
|
Mar 08:
|
Statistics of 2nd 2-class groups G22(K) of complex & real quadratic fields K
|
of type (2,2)
|
Frequency of Abelian, Dihedral, Quaternion, and Semidihedral Groups
|
|
Feb 25:
|
2nd order IPADs τp2(K) for fixed prime p = 2, resp. p = 3,
|
of complex quadratic fields
|
K = Q((-1780)1/2), K = Q((-2067)1/2), resp. K = Q((-3896)1/2)
|
|
Feb 19:
|
Complete normal lattice of three-stage 2-tower groups G23(K) of
|
type (2,4)
|
for complex quadratic fields K = Q((-1780)1/2) and K = Q((-2067)1/2)
|
|
Feb 17:
|
The first 50 complex quadratic fields Q(D1/2), -2408 ≤ D ≤ -260,
|
of type (2,4)
|
Transfer kernel and target types of 3 layers, result: 31 (62%) single stage 2-towers
|
|
Feb 06:
|
Discovery of a possible 3-class field tower group having three stages
|
for a TKT in Section F
|
namely of type F.11, first excited state, order 329, by M. F. Newman
|
|
Feb 03:
|
Discovery of possible 3-class field tower groups having three stages
|
for TKTs in Section F
|
27 of each type F.7,11,12,13, ground state, order 320, by M. F. Newman
|
|
Jan 03:
|
Criteria for Principal Factorization Types of dihedral fields of degree 2p,
|
α1,α2,α3,β1,β2,γ,δ1,δ2,ε,
|
based on integral representations of S-unit groups by Alex Bartel (Coventry)
|
|
2012
|
|
Nov 23:
|
Transfer kernels and targets of metabelian p-groups of order p5, type
|
(p,p), coclass 2, class 3
|
first commutator calculus for stem of isoclinism family Φ6, p+7 isomorphism classes
|
|
Oct 30:
|
Discovery of further 3-class field towers having three stages, such as
|
for k = Q((-262744)1/2)
|
of type E.14 in its 1st excited state, by M. R. Bush and D. C. Mayer
|
|
Oct 15:
|
Transfer kernels and targets of metabelian 7-groups of order 16807
|
(7,7), coclass 2, class 3
|
first commutator calculus for stem of isoclinism family Φ6, 14 isomorphism classes
|
|
Oct 11:
|
Non-metabelian 3-groups of order 38, class 5, coclass 3, derived length 3
|
which are Schur σ-groups
|
analysis of their lower and upper central series and pc-presentations
|
|
Sep 17:
|
Jahrestagung der DMV, Saarbrücken, BRD
|
Presentation
|
Abstract
|
|
Aug 24:
|
3-tower has length 3 for complex quadratic fields having same TKT/TTT
|
as k = Q((-9748)1/2)
|
proved by N. Boston, M. R. Bush and D. C. Mayer
|
|
Aug 23:
|
First faultless disproof of Scholz/Taussky's claim of 3-tower length 2
|
for k = Q((-9748)1/2)
|
by M. R. Bush and D. C. Mayer
|
|
Aug 17:
|
G22(k) of k = Q((-D)1/2) identified as descendant of <32,35>
|
for D = 9380, 14980
|
in a series of type (2,2,2) by Lemmermeyer, realizing family #79 by Newman/O'Brien
|
|
Aug 09:
|
Isomorphism of G32(B) and G32(k) for k = Q((-D)1/2)
|
when k of type (3,3)
|
20% inherited by lifting the entire 3-class field tower,
Strategic Operation on Nagasaki Day
|
|
Aug 06:
|
G32(B) for B = Q(D1/2,(-1)1/2), Gauss-Dirichlet type, D < 3*104
|
211 bicyclic biquadratic (3,3)
|
unique computation up to now,
Escalation of Nuclear War on Hiroshima Day
|
|
Jul 26:
|
Infinite pro-p Quantum Class Groups Gp∞(K) of finite abelianization
|
Transfer Kernels & Targets
|
Non-Abelian Cohen-Lenstra asymptotics: Arrigoni/Bembom/Bartholdy/Boston/Bush/Hajir
|
|
Jul 11:
|
G22(K) for 52 fields K = Q(D1/2,(-1)1/2) with 0 < D < 104
|
of type (2,2,2)
|
QCD (Quantum Chromo Dynamic) response to Zekhnini's thermonuclear bomb
|
|
Jun 14:
|
G52(M) of 5-dual cyclic quartic mirror images M = Q((ζ-ζ-1)D1/2)
|
of type (5,5)
|
of 34 real, resp. 4 complex quadratic fields Q(D1/2),
-16000 < D < 3500
|
|
Jun 07:
|
G32(B) = <27,2> abelian for 79% of B = Q(D1/2,(-3)1/2)
|
single stage 3-tower for (9,3)
|
all 73 (100%), resp. 236/316 (75%),
where Cl3Q(D1/2) = (9), resp. (3)
|
|
Jun 06:
|
G32(B) for B = Q(D1/2,(-3)1/2), D < 5*104
|
389 bicyclic biquadratic (9,3)
|
unique computation up to now (extension of Apr 07, 2012)
|
|
Jun 05:
|
G32(B) of order 6561 for B = Q(D1/2,(-3)1/2), D = 20521, 40156
|
(3,3) TKT b.10 (0043)
|
unique two examples where predicted twisting of bipolarization actually occurs
|
|
May 31:
|
G32(B) for B = Q(D1/2,(-3)1/2), D < 5*104
|
930 bicyclic biquadratic (3,3)
|
unique computation up to now (extension of Mar 07, 2012)
|
|
May 29:
|
Transfers of metabelian p-groups
|
Springer
|
Monatsh. Math. 166 (2012), no. 3 - 4, 467 - 495, DOI 10.1007/s00605-010-0277-x.
|
|
May 28:
|
Selection rules for triadic quantum class groups G = G32(B)
|
of B = Q(D1/2,(-3)1/2)
|
enforced by Kummer theory, Galois cohomology, automorphism groups Aut(G)
|
|
May 21:
|
G32(B) = <729,34> for B = Q(25891/2,(-3)1/2)
|
(3,3) TKT b.10 (0043)
|
Ascione's non-CF-group H, derived subgroup (3,3,3,3) instead of (9,3,3)
|
|
Apr 26:
|
International Workshop NTCCCS, Oujda, Morocco
|
Presentation
|
|
Apr 08:
|
G32(B) = <729,37> for B = Q(21771/2,(-3)1/2)
|
(3,3) TKT b.10 (0043)
|
Ascione's non-CF-group A, first triadic quantum class group of coclass 2
|
|
Apr 07:
|
G32(B) for B = Q(D1/2,(-3)1/2), Eisenstein type, D < 3*104
|
213 bicyclic biquadratic (9,3)
|
unique computation up to now, πoλεμos πατηρ παντων
|
|
Mar 07:
|
G32(B) for B = Q(D1/2,(-3)1/2), Eisenstein type, D < 3*104
|
549 bicyclic biquadratic (3,3)
|
unique computation up to now,
Initialization of Nuclear War "Ianna Bimetal"
(23592, 23994)
|
|
Feb 24:
|
The second p-class group of a number field
|
World Scientific
|
Int. J. Number Theory 8 (2012), no. 2, 471 - 505, DOI 10.1142/S179304211250025X.
|
|
Jan 25:
|
G32(K) = E↓4, E↓2 for K = Q(D1/2), D = 6540917, 8626101
|
(9,3) TKT b.15 (000;4)
|
second layer type (9,9,9,3), resp. (9,3,3,3), instead of (9,9,3,3)
|
|
2011
|
|
Dec 29:
|
G52(K) for K = Q(D1/2), D < 2*107
|
270 real (5,5)
|
unique computation up to now
|
|
Dec 23:
|
G52(K) for K = Q(D1/2), D > -2*106
|
813 complex (5,5)
|
unique computation up to now
|
|
Nov 04:
|
G52(K) = <3125,14> for K = Q((-89751)1/2)
|
(5,5) TKT (123456)
|
first realization of Taussky's fixed point principalization problem
|
|
Oct 31:
|
G32(K) = E↓4 for K = Q(37635801/2)
|
(9,3) TKT b.15 (000;4)
|
first realization of descendant of Ascione's CF-group E = <243,13>
|
|
Oct 27:
|
G32(K) = <2187,349> = H↓2 for K = Q(7003131/2)
|
(9,3) TKT b.15 (000;4)
|
first realization of descendant of Ascione's CF-group H = <243,14>
|
|
Sep 25:
|
Joint CSASC Conference, Krems, Austria
|
Presentation
|
|
Jul 29:
|
G32(K) for K = Q(D1/2), D < 107
|
271 real (9,3)
|
unique computation up to now
|
|
Jul 23:
|
G32(K) for K = Q(D1/2), D > -106
|
875 complex (9,3)
|
by far most extensive computation up to now
|
|
Jul 22:
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Transfer kernels and targets of metabelian 3-groups
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(9,3), coclass 2, class 3
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first commutator calculus for branch 1 of isoclinism family Φ3
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Jul 09:
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Transfer kernels and targets of metabelian 3-groups
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(9,3), coclass 3, class 3
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first commutator calculus for branch 1 of isoclinism family Φ6
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Jul 01:
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27th Journées Arithmétiques, Vilnius, Lithuania
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Presentation
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Abstract
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2010
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Nov 08:
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Transfer kernels and targets of metabelian 5-groups of order 3125
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(5,5), coclass 2, class 3
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first commutator calculus for stem of isoclinism family Φ6, 12 isomorphism classes
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Sep 27:
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Journées de Théorie des Nombres, Oujda, Morocco
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Presentation
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Reference
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Jul 25:
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G32(K) for K = Q(D1/2), D > -106
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2020 complex (3,3)
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by far most extensive computation up to now
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Mar 31:
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G32(K) for K = Q(D1/2), D < 107
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2576 real (3,3)
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by far most extensive computation up to now (extension of Dec 17, 2009)
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Mar 20:
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Transfer kernels of type d (.043) or d* (0.43) of metabelian 3-groups
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(3,3), coclass ≥ 3
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supplementary commutator calculus to distinguish terminal and capable vertices
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Mar 18:
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G32(K) for K = Q(84917131/2)
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(3,3) TKT d*.25 (0143)
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first triadic quantum class group of coclass 4 over real quadratic base field
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2009
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Dec 17:
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G32(K) for K = Q(D1/2), D < 106
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149 real (3,3)
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by far most extensive computation up to now
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Dec 07:
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Top Down Principalization Algorithm
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via class group structure
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complete determination of 3-class groups of type (3,3,3) of unramified S3 fields
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Nov 09:
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G32(K) for K = Q(7106521/2)
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(3,3) TKT b.10 (0043)
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first triadic quantum class group of coclass 3 over real quadratic base field
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Nov 04:
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Transfer kernels of metabelian p-groups
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(p,p), coclass 1
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first commutator calculus for primes p greater than or equal to 5
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Nov 02:
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Transfer kernels of metabelian 2-groups
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(2,2), coclass 1
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first explicit commutator calculus for exceptional prime p = 2
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Sep 25:
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Jahrestagung der ÖMG und DMV, Graz, Austria
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Presentation
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Abstract
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2008
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Jan 01:
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G32(K) = <729,54> for K = Q(5403651/2)
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(3,3) TKT c.21 (0231)
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first realization of capable vertex by triadic quantum class group over real quadratic field
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2006
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Jan 30:
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G32(K) = <729,57> for K = Q(2147121/2)
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(3,3) TKT G.19 (2143)
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first triadic quantum class group of coclass 2 over real quadratic base field
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