Two groups with isomorphic group algebras
type: Item
instance of: scholarly article
title: Two groups with isomorphic group algebras
zbMATH Open document ID: 0674.20001
DOI: 10.1007/BF01199112
author: Gabriel Navarro
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Suppose that G and H are finite groups. If \({\mathbb{C}}G\cong {\mathbb{C}}H\), I. M. Isaacs proved that the nilpotency of G implies the nilpotency of H. In this paper it is proved the modular version of the above result, when \({\mathbb{C}}\) is replaced by an algebraically closed field of positive characteristic. Also, a well known Theorem of Thompson on character degrees is obtained for Brauer characters: Let G be a p-solvable group and \(q\neq p\) a prime number. If q divides \(\phi\) (1) for all \(\phi\) nonlinear irreducible p-Brauer characters of G, then G has a normal q- complement.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4103324
zbMATH Keywords: isomorphism problem
zbMATH Keywords: finite groups
zbMATH Keywords: nilpotency
zbMATH Keywords: character degrees
zbMATH Keywords: Brauer characters
zbMATH Keywords: p-solvable group
zbMATH Keywords: normal q-complement
reviewed by: J. Navarro
MaRDI profile type: Publication
cites work: Q3955560
cites work: Q3934684
cites work: Character Degrees and Derived Length of a Solvable Group
cites work: Recovering information about a group from its complex group algebra
cites work: On the projectives of a group algebra
description: scientific article; zbMATH DE number 4103324