The Prime Number Year 2017

Maximal Unramified Pro-p Extensions of Number Fields

explored with the aid of

Structured Descendant Trees of Finite p-Groups



Karl-Franzens University Graz, left side


Recent International Conferences

January 13 - 15, 2018:
3rd International Conference
on Groups and Algebras
ICGA 2018, Sanya, China
Invited Lecture:
Deep Transfers
of p-Class Tower Groups

November 11 - 12, 2016:
International Colloquium of Algebra,
Number Theory, Cryptography,
and Information Security
ANCI 2016, Taza, Morocco
Invited Keynote:
Recent Progress in Determining
p-Class Field Towers

July 25 - 27, 2016:
2nd International Conference
on Groups and Algebras
ICGA 2016, Suzhou, China
Presentation:
p-Capitulation over Number Fields
with p-Class Rank Two

July 19 - 21, 2015:
1st International Conference
on Groups and Algebras
ICGA 2015, Shanghai, China
Presentation:
Periodic Sequences
of p-Class Tower Groups


Karl-Franzens University Graz, centre with 8 figures


Publications and Preprints 2017

Successive approximation of p-class towers
Deep transfers of p-class tower groups
Propagation of Artin patterns between isoclinic 2-groups
Modeling rooted in-trees by finite p-groups
Quintic reflection and 5-class towers
Number fields with transfer kernel type F
Final report on p-class towers
Recent progress in determining p-class towers

Background and Aims

We investigate the Hilbert p-class field tower F(p,∞,K) of algebraic number fields K
within the frame of our International Scientific Research Project with title
Towers of p-class fields over algebraic number fields,
supported by the Austrian Science Fund (FWF): P 26008-N25 .

  1. The metabelianization G/G'' of the Galois group G of the p-class tower,
    describes the lowest two stages of the tower,
    K < F(p,1,K) < F(p,2,K).
  2. Recently, we pushed forward beyond the two-stage towers into the strange realm of
    non-metabelian p-groups with derived length 3,
    K < F(p,1,K) < F(p,2,K) < F(p,3,K),
    thereby advancing Austrian Science
    to the Forefront of International Research.



Karl-Franzens University Graz, right side


International Research Project


Daniel C. Mayer
Principal investigator of the
International Research Project
Towers of p-Class Fields
over Algebraic Number Fields
supported by the Austrian Science Fund (FWF):
P26008-N25

Time Schedule:




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Web master's e-mail address:
contact@algebra.at
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IPAD and IPOD 2016
29ièmes Journées Arithmétiques 2015
Fame For Styria 2014
Research Frontier 2013
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