Computing a spectral sequence of finite Heisenberg groups of prime power order

被引：0

作者：

Ocana, Oihana Garaialde ^{[1
]}

Sanchez, Lander Guerrero ^{[1
]}

机构：

[1] Euskal Herriko Unibertsitatea, Matemat Saila, Zientzia & Teknol Fak, Posta Kutxa 644, Bilbao 48080, Spain

来源：

JOURNAL OF ALGEBRA | 2023年 / 620卷

关键词：

Spectral sequence; Cohomology ring; Finite p -groups; COHOMOLOGY;

D O I：

10.1016/j.jalgebra.2022.11.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p > 5 be a prime number, let n > 2 be a natural number and let Heis(pn) denote the Heisenberg group modulo pn. We study the Lyndon-Hochschild-Serre spectral sequence E(Heis(pn)) associated to Heis(pn) considered as a split extension, and show that, E(Heis(pn)) collapses in the third page. Moreover, for a fixed p, the spectral sequences E(Heis(pn)) are isomorphic as bigraded algebras from the second page on.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：558 / 584

页数：27

共 37 条

[1] Subgroup congruences for groups of prime power order [J].

Aivazidis, Stefanos ;

Loukaki, Maria .

JOURNAL OF ALGEBRA, 2022, 610 :818-830

[2] A classification of the finite 2-generator cyclic-by-abelian groups of prime-power order [J].

Broche, Osnel ;

Garcia-Lucas, Diego ;

del Rio, Angel .

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2023, 33 (04) :641-686

[3] On the multiple holomorph of groups of squarefree or odd prime power order [J].

Tsang, Cindy .

JOURNAL OF ALGEBRA, 2020, 544 :1-28

[4] Groups of prime-power order with a small second derived quotient [J].

Schneider, C .

JOURNAL OF ALGEBRA, 2003, 266 (02) :539-551

[5] Finite-order formulation of Vinogradov's C-spectral sequence [J].

Vitolo, R .

ACTA APPLICANDAE MATHEMATICAE, 2002, 72 (1-2) :133-154

[6] Finite-Order Formulation of Vinogradov's C-Spectral Sequence [J].

Raffaele Vitolo .

Acta Applicandae Mathematica, 2002, 72 :133-154

[7] Large odd prime power order automorphism groups of algebraic curves in any characteristic [J].

Korchmaros, Gabor ;

Montanucci, Maria .

JOURNAL OF ALGEBRA, 2020, 547 :312-344

[8] ON QUANDLE HOMOLOGY GROUPS OF ALEXANDER QUANDLES OF PRIME ORDER [J].

Nosaka, Takefumi .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (07) :3413-3436

[9] A spectral sequence for the homology of a finite algebraic delooping [J].

Richter, Birgit ;

Ziegenhagen, Stephanie .

JOURNAL OF K-THEORY, 2014, 13 (03) :563-599

[10] Surface braid groups, finite Heisenberg covers and double Kodaira fibrations [J].

Causin, Andrea ;

Polizzi, Francesco .

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2021, 22 (03) :1309-1352

← 1 2 3 4 →