The modular group algebra of a central-elementary-by-abelian p-group
type: Item
instance of: scholarly article
title: The modular group algebra of a central-elementary-by-abelian p-group
zbMATH Open document ID: 0632.16011
DOI: 10.1007/BF01197966
author: Robert Sandling
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: The title refers to a p-group G for which \(\gamma _ 2(G)^ p\gamma _ 3(G)=1\) where \(\gamma _ n(G)\) is the n-th term of the lower central series of G. Two results are proved about the modular group algebra FG, where F is the field of p elements and G is a p-group: FG determines the isomorphism type of \(G/\gamma _ 2(G)^ p\gamma _ 3(G)\); there is a normal complement to G in the group of units of FG if G is central- elementary-by-abelian. Some partial results are stated for the broader class of elementary-abelian-by-abelian p-groups.
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 4027695
zbMATH Keywords: lower central series
zbMATH Keywords: modular group algebra
zbMATH Keywords: normal complement
zbMATH Keywords: group of units
zbMATH Keywords: elementary-abelian-by-abelian p-groups
zbMATH Keywords: isomorphism problem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4027695