29 Journees Arithmetiques 2015

IPADs of p-Tower Groups

Debreceni Egyetem
University of Debrecen
Lajos Kossuth, Debrecen
Lajos Kossuth Monument, Debrecen
Great Protestant Church
Great Protestant Church
Debreceni Egyetem
University of Debrecen
City Line 2, Debrecen
City Line 2, Main Railway Station

My first words written in the
New Year 2015
are entirely devoted to the
29th Journées Arithmétiques
which will take place at the
University of Debrecen
(Debreceni Egyetem).

My contributed presentation with title
Index-p Abelianization Data of p-Class Tower Groups
(briefly: IPADs of p-Tower Groups)
will introduce a series of sophisticated new techniques
for identifying the second p-class group Gp2(K)
(the Galois group of the maximal metabelian unramified p-extension)
or even the p-class tower group Gp(K) of a number field K
(the Galois group of the maximal unramified pro-p extension):
  • pattern recognition via Artin transfers,
  • multiple-layered transfer kernel types (TKTs),
  • multiple-layered transfer target types (TTTs),
  • iterated IPADs of second order,
  • arithmetically structured coclass trees of finite p-groups,
  • uni-polarization and stabilization in coclass trees,
  • periodic multifurcations in descendant trees,
  • mainline principle of polycyclic pc-presentations,
  • and various kinds of pruning strategies.

One of the definite highlights will be a
Main Theorem which gives a complete overview of all possible
IPADs and multilayered TTTs of a number field K
with 3-class group Cl3(K) of type (3,3)
together with pc-presentations for the corresponding
metabelianization G/G'' of the 3-tower group G of K.

Debreceni Egyetem
University of Debrecen
(formerly: Lajos Kossuth Egyetem)
located in the Campus (Egyetemváros)
beside the City Forest (Nagyerdö)

29th Journées Arithmétiques 2015

July 6 -- 10

Old Committee House
Old Committee House

Debreceni Egyetem
University of Debrecen
Lajos Kossuth, Budapest
Lajos Kossuth Monument, Budapest
Szent Anna Piarist Church
Szent Anna Piarist Church
Lajos Kossuth Haydut
Fourrage by Lajos Kossuth Hajdús

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