A Sylowlike theorem for integral group rings of finite solvable groups
type: Item
instance of: scholarly article
title: A Sylowlike theorem for integral group rings of finite solvable groups
zbMATH Open document ID: 0793.20005
DOI: 10.1007/BF01194231
author: Klaus W. Roggenkamp
author: Wolfgang Kimmerle
published in: Archiv der Mathematik
publication date: 1994-05-24T00:00:00Z
review text: Let \(G\) and \(H\) be finite solvable groups with \(\mathbb{Z} G = \mathbb{Z} H\) as augmented algebras. If \(S\) is a Sylow \(p\)-subgroup of \(H\), then there exists a unit \(a \in \mathbb{Q} G\) such that \(aSa^{-1}\) is a Sylow \(p\)- subgroup of \(G\).
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 571890
zbMATH Keywords: finite solvable groups
zbMATH Keywords: augmented algebras
zbMATH Keywords: Sylow \(p\)-subgroup
zbMATH Keywords: unit
MaRDI profile type: Publication
cites work: Q3934684
cites work: Q3659962
cites work: Q3481920
cites work: Isomorphic groups and group rings
cites work: Isomorphisms of p-adic group rings
cites work: Q3679372
cites work: Q4071907
Recommended article: The structure of the integral grouping of a finite group with cyclic sylow subgroups
Recommended article: Integral group rings whose group of units is solvable an elementary proof
Recommended article: A structure theorem for the unit group of the integral group ring of some finite groups
Recommended article: On rings of quotients of group algebras of soluble groups of finite rank
Recommended article: On theorems of Sylow type for finite groups
Recommended article: Integral group rings of solvable groups with trivial central units
Recommended article: A Sylow theorem for the integral group ring of \(\mathrm{PSL}(2,q)\)
Recommended article: A Finite Index Property of Certain Solvable Groups
Recommended article: On the isomorphism problem for integral group rings of finite groups
Recommended article: Q4012099
description: scientific article; zbMATH DE number 571890