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Chronicle and Time Schedule
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August 2013
|
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Aug 09:
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Groups St Andrews 2013, Fife, Scotland
|
Presentation
|
Abstract
,
Finite 3-groups as viewed from class field theory
|
|
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)
|
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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 25:
|
Complete Proposal for the CIMPA - UNESCO Course "CIMPA 2015 Oujda"
|
Summary
|
Computational Number Theory and its Applications in Cryptography
|
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Aug 30:
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French translation of the CIMPA - UNESCO Lectures "CIMPA 2015 Oujda"
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Resumé
|
Théorie des Nombres Algorithmique et Applications en Cryptographie
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September 2013
|
|
Sep 01:
|
Official Start of our International Research Project
|
FWF: P 26008-N25
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Towers of p-Class Fields over Algebraic Number Fields
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Sep 23:
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ÖMG and DMV Congress 2013, Innsbruck, Austria
|
Presentation
|
Abstract
,
3-class field towers of exact length 3
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|
October 2013
|
|
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
|
|
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 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.
|
|
November 2013
|
|
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>
|
|
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 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
|
|
December 2013
|
|
Dec 18:
|
West Coast Number Theory 2013, Asilomar, Monterey, California
|
Presentation
|
Class towers and capitulation over quadratic fields
|
|
January 2014
|
|
Jan 31:
|
On the strongly ambiguous classes of k|Q(i) where k = Q((2p1p2)1/2,i)
|
Report
|
of a paper by A. Azizi, A. Zekhnini, and M. Taous, in Asian-European Journal of Mathematics
|
|
February 2014
|
|
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.
|
|
March 2014
|
|
Mar 27:
|
Annual Report 2013 for the Austrian Science Fund (FWF)
|
Report
|
Stand-alone research project P 26008-N25
|
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April 2014
|
|
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
|
|
May 2014
|
|
May 21:
|
Descendant trees of finite p-groups
|
Article
|
Nuclear rank, multifurcation, coclass graphs, parametrized pc-presentations
|
|
May 28:
|
Strategy of pattern recognition via Artin transfers
|
Preprint
|
Arithmetical applications of: commutative Artin diagram, inheritance from quotients
|
|
June 2014
|
|
Jun 16:
|
Artin transfers and structured descendant trees
|
Article
|
Inheritance from quotients, stabilization criteria, and pattern recognition
|
|
July 2014
|
|
Jul 05:
|
Principalization in algebraic number theory
|
Article
|
Artin reciprocity law, commutative Artin diagram, and Galois cohomology
|
|
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 19:
|
Complex quadratic fields of type (3,3,3)
|
Preprint
|
Infinite 3-class tower, transfer kernels and targets, and second 3-class group
|
|
Jul 31:
|
p-group generation algorithm
|
Article
|
P-covering group, nucleus, allowable subgroups, orbits, step sizes
|
|
August 2014
|
|
Aug 27:
|
Structural interpretation of composite Artin transfers
|
Article
|
Wreath product of symmetric groups Sm and Sn with respect to {1,…,n}
|
|
September 2014
|
|
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
|
|
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 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)
|
|
October 2014
|
|
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.
|
|
Oct 23:
|
Principalization algorithm via class group structure
|
CEDRAM
|
J. Théor. Nombres Bordeaux 26 (2014), no. 2, 415 - 464.
|
|
November 2014
|
|
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.
|
|
December 2014
|
|
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.
|
|
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
|
|
January 2015
|
|
Jan 27:
|
Periodic bifurcations in descendant trees of finite p-groups
|
Adv. Pure Math.
|
5 (2015), no. 4, 162-195, Special Issue on Group Theory, DOI 10.4236/apm.2015.54020
|
|
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
|
by A. Azizi, A. Zekhnini, and M. Taous, in Journal of Algebra and its Applications
|
|
February 2015
|
|
Feb 18:
|
Index-p abelianization data of p-class tower groups
|
Adv. Pure Math.
|
5 (2015), no. 5, 286-313, Special Issue on Number Theory and Cryptography, DOI 10.4236/apm.2015.55029
|
|
Feb 25:
|
Annual Report 2014 for the Austrian Science Fund (FWF)
|
Report
|
Stand-alone research project P 26008-N25
|
|
March 2015
|
|
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
|
|
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
|
|
April 2015
|
|
May 2015
|
|
May 18:
|
École de Recherche CIMPA UNESCO 2015
|
Oujda, Morocco
|
La théorie algorithmique des nombres (lectures and exercises)
|
|
June 2015
|
|
July 2015
|
|
Jul 09:
|
29th Journées Arithmétiques (JA) 2015, Debrecen, Hungary
|
Presentation
|
Index-p abelianization data of p-class tower groups
|
|
Jul 21:
|
1st International Conference on Groups and Algebras (ICGA) 2015, Shanghai, China
|
Presentation
|
Invited Lecture on Periodic sequences of p-class tower groups
|
|
August 2015
|
|
Aug 31:
|
22nd Czech and Slovak International Conference on Number Theory (CSICNT) 2015, Liptovský Ján, Slovakia
|
Presentation
|
New number fields with known p-class tower
|
|
September 2015
|
|
Sep 30:
|
New number fields with known p-class tower
|
Tatra Mountains Math. Publ.
|
64 (2015), 21-57
|
|
October 2015
|
|
Oct 18:
|
Induced homomorphism (quotient group)
|
Article
|
induced homomorphism, characteristic subgroups, GI-automorphisms, functorial properties
|
|
November 2015
|
|
Nov 12:
|
Grunwald-Wang theorem, an effective version
|
Math. Rev. 3368167
|
of a paper by S. Wang, in Sci. China Math.
|
|
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
|
|
December 2015
|
|
January 2016
|
|
February 2016
|
|
Feb 18:
|
Annual Report 2015 for the Austrian Science Fund (FWF)
|
Report
|
Stand-alone research project P 26008-N25
|
|
Feb 28:
|
On class groups of imaginary quadratic fields
|
Math. Rev. 3404031
|
of a paper by A. Wiles, in J. London Math. Soc.
|
|
March 2016
|
|
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
|
|
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
|
|
April 2016
|
|
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
|
|
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
|
|
May 2016
|
|
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
|
|
June 2016
|
|
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
|
|
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 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 28:
|
18th Postgraduate Group Theory Conference
|
Imperial College, London
|
Presentation Three-Stage Towers of 5-Class Fields, London, UK
|
|
July 2016
|
|
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
|
|
August 2016
|
|
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)
|
|
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 31:
|
Official End of our International Research Project
|
FWF: P 26008-N25
|
Towers of p-Class Fields over Algebraic Number Fields
|
|
September 2016
|
|
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
|
|
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
|
|
October 2016
|
|
November 2016
|
|
Nov 11:
|
1st 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
|
