Chronicle and Time Schedule

August 2013

Aug 09:

Groups St Andrews 2013, Fife, Scotland

Presentation

Abstract
,
Finite 3groups as viewed from class field theory

Aug 19:

Generalization of our lecture at "Groups Saint Andrews 2013"

Preprint

PCPresentations for infinite periodic sequences of 3groups G, G/G' ≅ (9,3)

Aug 22:

Inspired by some presentations at "Groups St Andrews 2013":

Preprint

Complete Normal Lattice of metabelian pgroups 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

Aug 30:

French translation of the CIMPA  UNESCO Lectures "CIMPA 2015 Oujda"

Resumé

Théorie des Nombres Algorithmique et Applications en Cryptographie

September 2013

Sep 01:

Official Start of our International Research Project

FWF: P 26008N25

Towers of pClass Fields over Algebraic Number Fields

Sep 23:

ÖMG and DMV Congress 2013, Innsbruck, Austria

Presentation

Abstract
,
3class field towers of exact length 3

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(D^{1/4})

by means of calculating the relative norms of a fundamental system of units

Oct 25:

Units of pure quartic fields Q(p^{1/4}) with p ≡ 7 (mod 16)

Math. Rev. 3059109

of a paper by A. AguilarZavoznik and M. PinedaRuelas, 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(D^{1/3})

into principal factorization types, according to Barrucand / Cohn

Nov 17:

Classification into principal factorization types of pure quintic fields

Q(D^{1/5})

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 kQ(i) where k = Q((2p_{1}p_{2})^{1/2},i)

Report

of a paper by A. Azizi, A. Zekhnini, and M. Taous, in AsianEuropean 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

Standalone research project P 26008N25

April 2014

Apr 12:

Principalization of 2class groups of type (2,2,2) of biquadratic fields

k = Q((1)^{1/2},d^{1/2}), d = p_{1}p_{2}q

in cooperation with A. Azizi, A. Zekhnini, and M. Taous, in IJNT

May 2014

May 21:

Descendant trees of finite pgroups

Article

Nuclear rank, multifurcation, coclass graphs, parametrized pcpresentations

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 2class field tower of some abelian 2extensions 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 3class tower, transfer kernels and targets, and second 3class group

Jul 31:

pgroup generation algorithm

Article

Pcovering group, nucleus, allowable subgroups, orbits, step sizes

August 2014

Aug 27:

Structural interpretation of composite Artin transfers

Article

Wreath product of symmetric groups S_{m} and S_{n} with respect to {1,…,n}

September 2014

Sep 16:

Completely new perspective of the population of coclass trees T_{2}(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 3groups 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 pgroups G having G/G' = (p^{2},p^{2}) or (p^{3},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 pring 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 2class groups of type (2,2,2) of biquadratic fields
Q((p_{1}p_{2}q)^{1/2},(1)^{1/2})

World Scientific

Int. J. Number Theory 11 (2015), no. 4, 11771215, DOI 10.1142/S1793042115500645,
in cooperation with A. Azizi, A. Zekhnini and M. Taous.

Dec 10:

The group Gal(k_{3}^{(2)}k) for k = Q((3)^{1/2},d^{1/2}) 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 pgroups

Adv. Pure Math.

5 (2015), no. 4, 162195, Special Issue on Group Theory, DOI 10.4236/apm.2015.54020

Jan 30:

Coclass of Gal(k_{2}^{(2)}k) for some fields k = Q((p_{1}p_{2}q)^{1/2},(1)^{1/2}) with 2class 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:

Indexp abelianization data of pclass tower groups

Adv. Pure Math.

5 (2015), no. 5, 286313, 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

Standalone research project P 26008N25

March 2015

Mar 08:

Descendants of <64,75> as second 2class groups of biquadratic Dirichlet fields

Q((1)^{1/2},d^{1/2})

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

Indexp abelianization data of pclass tower groups

Jul 21:

1st International Conference on Groups and Algebras (ICGA) 2015, Shanghai, China

Presentation

Invited Lecture on Periodic sequences of pclass 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 pclass tower

September 2015

Sep 30:

New number fields with known pclass tower

Tatra Mountains Math. Publ.

64 (2015), 2157

October 2015

Oct 18:

Induced homomorphism (quotient group)

Article

induced homomorphism, characteristic subgroups, GIautomorphisms, functorial properties

November 2015

Nov 12:

GrunwaldWang 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 pgroups

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

Standalone research project P 26008N25

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 pClass 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 < 10^{8}, by far most extensive computation up to now

April 2016

Apr 07:

Sensational discovery of the first 5CLASS 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 5Sylow subgroup of the symmetric group of degree 25 as

2nd 5class group

Occurrence for the real quadratic field with discriminant d = 27186289

May 2016

May 30:

Recent Progress in Determining pClass 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 10^{7} < d, by far most extensive computation up to now

Jun 15:

Annihilator Ideals of TwoGenerated Metabelian pGroups

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 3groups G_{3}^{2}K with Kernel Type F and Coclass 6 over quadratic fields K

Jun 28:

18th Postgraduate Group Theory Conference

Imperial College, London

Presentation ThreeStage Towers of 5Class Fields, London, UK

July 2016

Jul 25:

2nd International Conference on Groups and Algebras

ICGA, Suzhou

Invited Lecture
on pCapitulation over Number Fields with pClass Rank Two, Suzhou, China

August 2016

Aug 09:

5Principalization Type and Second 5Class Group

Gal(F_{5}^{2}M/M)

of all Cyclic Quartic 5Mirror Fields M=Q((ζζ^{1})d^{1/2}), d < 10000, with 5Class Group (5,5)

Aug 20:

Long desired discovery of a Second 5Class Group of Elevated Coclass

cc(G_{5}^{2}M) ≥ 3

for the Cyclic Quartic 5Mirror Field M=Q((ζζ^{1})d^{1/2}) with d = 8689

Aug 31:

Official End of our International Research Project

FWF: P 26008N25

Towers of pClass Fields over Algebraic Number Fields

September 2016

Sep 07:

3Principalization Type and Second 3Class Group

Gal(F_{3}^{2}K/K)

of all Cyclic Cubic Fields K with 3Class Group (3,3) and Conductor c < 100000

Sep 08:

Sensational Discovery of the First ThreeStage Tower

F_{3}^{∞}K/K

of 3Class 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 pClass Field Towers, Taza, Morocco
