Units of commutative modular group algebras
type: Item
instance of: scholarly article
title: Units of commutative modular group algebras
zbMATH Open document ID: 0806.16033
DOI: 10.1016/0022-4049(94)90031-0
author: P. Hill
published in: Journal of Pure and Applied Algebra
publication date: 1994-08-07T00:00:00Z
review text: Let \(FG\) be the group algebra of an abelian \(p\)-group \(G\) over a perfect field \(F\) of characteristic \(p\). The direct factor problem is whether \(G\) is a direct factor of the group V(G) of the normalized units of the unit group \(U(G)\) of \(FG\). This problem has a positive solution if \(V(G)/G\) is simply presented. In the paper under review the author proves that \(V(G)/G\) has a \(\nu\)-basis. Recently the author has established that any abelian \(p\)-group \(A\) with a \(\nu\)-basis such that \(| A| \leq \aleph_ 1\) is simply presented. It is still an open problem whether a group \(A\) with a \(\nu\)-basis is simply presented if \(| A | > \aleph_ 1\).
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 612145
zbMATH Keywords: group of normalized units
zbMATH Keywords: simply presented \(p\)-group
zbMATH Keywords: group algebra
zbMATH Keywords: abelian \(p\)-group
zbMATH Keywords: direct factor problem
zbMATH Keywords: unit group
zbMATH Keywords: \(\nu\)-basis
reviewed by: Todor Mollov
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90031-0
OpenAlex ID: W2014649980
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description: scientific article; zbMATH DE number 612145