The splitting data of cohomology classes
type: Item
instance of: scholarly article
title: The splitting data of cohomology classes
zbMATH Open document ID: 0547.20048
DOI: 10.1007/BF01229324
author: Leo Corry
author: Shmuel Rosset
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: Let G be a finite group, M a G module and assume given \(\alpha \in\hat H^*(G,M)\) (Tate cohomology). The splitting data of \(\alpha\) is defined to be the set of subgroups of G to which the restriction of \(\alpha\) is zero. In this paper the main properties of the splitting data are pointed out, and it is shown that given a set of subgroups of G, satisfying the mentioned properties, it is possible for any \(k\in {\mathbb{Z}}\), to construct a G-module M and an element \(\alpha\) of \(\hat H^ k(G,M)\), such that the given set of subgroups is the splitting data of \(\alpha\). Some restrictions can be imposed as to the order of \(\alpha\). For \(k=2\), we obtain group extensions which furnish interesting examples related to the ''ranks'' of crossed products.
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 3871659
zbMATH Keywords: Tate cohomology
zbMATH Keywords: restriction
zbMATH Keywords: splitting data
zbMATH Keywords: G-module
zbMATH Keywords: group extensions
zbMATH Keywords: crossed products
MaRDI profile type: Publication
cites work: Group extensions and division algebras
cites work: The goldie rank of virtually polycyclic groups
full work available at URL: https://doi.org/10.1007/bf01229324
OpenAlex ID: W2048887264
description: scientific article; zbMATH DE number 3871659