COMPUTATION OF LOW-DIMENSIONAL (CO) HOMOLOGY GROUPS FOR INFINITE SEQUENCES OF p-GROUPS WITH FIXED COCLASS

被引：8

作者：

Eick, Bettina ^{[1
]}

Feichtenschlager, Doerte ^{[1
]}

机构：

[1] Tech Univ Carolo Wilhelmina Braunschweig, Inst Computat Math, Braunschweig, Germany

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2011年 / 21卷 / 04期

关键词：

p-groups; coclass; Schur multiplicator; cohomology; symbolic computation;

D O I：

10.1142/S021819671100639X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Eick and Leedham-Green introduced infinite sequences of p-groups of fixed coclass. Here we describe an algorithm to compute the Schur multiplicators of all groups in an infinite sequence simultaneously. Based on this, we prove that these Schur multiplicators can be described by a single parametrised presentation; this confirms a conjecture by Eick. Similar results are obtained for certain low-dimensional cohomology groups; these results support a conjecture by Carlson.

引用

页码：635 / 649

页数：15

共 15 条

[1]

[Anonymous], 2004, GAP GROUPS ALGORITHM

[2] Coclass and cohomology [J].

Carlson, JF .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2005, 200 (03) :251-266

[3]

Dietrich H, 2008, CONTEMP MATH, V470, P45

[4]

du Sautoy M., 2001, I HAUTES ETUDES SCI, V92, P63

[5]

Eick B., INFINITE SEQUENCES F

[6] Schur multiplicators of finite p-groups with fixed coclass [J].

Eick, Bettina .

ISRAEL JOURNAL OF MATHEMATICS, 2008, 166 (01) :157-166

[7] Computing the Schur multiplicator and the nonabelian tensor square of a polycyclic group [J].

Eick, Bettina ;

Nickel, Werner .

JOURNAL OF ALGEBRA, 2008, 320 (02) :927-944

[8] On the classification of prime-power groups by coclass [J].

Eick, Bettina ;

Leedham-Green, Charles .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2008, 40 :274-288

[9]

Holt Derek F., 2005, Handbook of computational group theory. Discrete Mathematics and its Applications

[10]

LEEDHAMGREEN C, 2002, LONDON MATH SOC MONO

← 1 2 →