Fusion of \(\pi\)-subgroups, isometries, and normal complements
type: Item
instance of: scholarly article
title: Fusion of \(\pi\)-subgroups, isometries, and normal complements
zbMATH Open document ID: 0617.20003
DOI: 10.1016/0021-8693(87)90121-9
author: Geoffrey R. Robinson
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The stated aim of the paper is ''to isolate some group-theoretic requirements which will ensure that a subgroup, H, of the finite group G will control the conjugacy of certain of its elements, in such a manner that generalized characters of H will extend to generalized characters of G.'' The type of result obtained is exemplified by Lemma 2: Let H be a subgroup of group G such that H controls elementary \(\pi\)-fusion for some set of primes, \(\pi\). Then (i) any generalized character of H which is constant on \(\pi\)-sections may be extended in a unique fashion to a generalized character of G which is constant on \(\pi\)-sections, and (ii) \(O^{\pi}(G)\cap H=O^{\pi}(H)\). (Note: A subgroup H of finite group G is said to control elementary \(\pi\)-fusion in G if, for every Brauer elementary \(\pi\)-subgroup E of H, \(N_ G(E)=C_ G(E)N_ H(E)\), and, for every \(\pi\)-element x of H, \([C_ G(x):C_ H(x)]\) is a (\(\pi\) '\(\cup \pi (x))\)-number.)
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 4000193
zbMATH Keywords: generalized characters
zbMATH Keywords: elementary \(\pi \)-fusion
zbMATH Keywords: \(\pi \)-sections
reviewed by: W. E. Deskins
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90121-9
OpenAlex ID: W2033360748
cites work: Q5185241
cites work: On normal complements to sections of finite groups
cites work: Blocks, Isometries, and Sets of Primes
description: scientific article; zbMATH DE number 4000193