A modular version of Maschke's theorem for groups with cyclic \(p\)-Sylow subgroups
type: Item
instance of: scholarly article
title: A modular version of Maschke's theorem for groups with cyclic \(p\)-Sylow subgroups
zbMATH Open document ID: 0804.20006
published in: Journal of Algebra
publication date: 1995-01-12T00:00:00Z
review text: A deformation \(A_ 1\) of an algebra \(A_ 0\) is an algebra which is a specialization of a multiplication structure \(A(t)\) depending on a parameter \(t\) such that \(A(0)\) is isomorphic to \(A_ 0\) and for almost all values \(s\) of \(t\) \(A(s)\) are isomorphic to \(A_ 1\). Let \(k[G]\) be the group algebra of a finite group \(G\) over an algebraically closed field \(k\) of characteristic \(p\) dividing the order of \(G\). The author proves that for every block of a cyclic defect group there exists a semisimple deformation. As a corollary it is obtained the existence of a semisimple deformation of \(k[G]\) if \(G\) has cyclic \(p\)-Sylow subgroups.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S80
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 554139
zbMATH Keywords: group algebras
zbMATH Keywords: finite groups
zbMATH Keywords: blocks
zbMATH Keywords: cyclic defect groups
zbMATH Keywords: semisimple deformations
zbMATH Keywords: cyclic \(p\)-Sylow subgroups
author: Mary Schaps
reviewed by: S. D. Kozlov
MaRDI profile type: Publication
full work available at URL: jabr.1994.1034
OpenAlex ID: W2019990171
DOI: 10.1006/JABR.1994.1034
description: scientific article; zbMATH DE number 554139