On the isomorphism problem for integral group rings of finite groups
type: Item
instance of: scholarly article
title: On the isomorphism problem for integral group rings of finite groups
zbMATH Open document ID: 0793.20006
DOI: 10.1007/BF01194844
author: Klaus W. Roggenkamp
author: Alexander Zimmermann
published in: Archiv der Mathematik
publication date: 1994-05-24T00:00:00Z
review text: We give a positive answer to the isomorphism problem for a class of groups \(G\) containing those with abelian normal subgroup \(N\) and nilpotent \(G/N\). The proof depends on a result of the first author in collaboration with L. L. Scott that guarantees that group bases of \(p\)- adic group rings of \(p\)-solvable groups \(G_ p\) without normal subgroup of order relatively prime to \(p\) are conjugate. Our result also covers groups being certain abelian extensions of direct products of groups \(G_ p\) satisfying some additional constraints.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C10
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 572360
zbMATH Keywords: finite groups
zbMATH Keywords: isomorphism problem
zbMATH Keywords: group bases
zbMATH Keywords: \(p\)-adic group rings
zbMATH Keywords: \(p\)-solvable groups
reviewed by: Alexander Zimmermann
MaRDI profile type: Publication
cites work: Endliche Gruppen I
cites work: Isomorphisms of p-adic group rings
cites work: Q3804887
full work available at URL: https://doi.org/10.1007/bf01194844
OpenAlex ID: W4249039520
description: scientific article; zbMATH DE number 572360