On the intersection of a class of maximal subgroups of a finite group. II
type: Item
instance of: scholarly article
title: On the intersection of a class of maximal subgroups of a finite group. II
zbMATH Open document ID: 0597.20014
DOI: 10.1016/0022-4049(86)90074-5
author: Prabir Bhattacharya
author: N. P. Mukherjee
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: In this paper the authors continue their study [Part I, to appear] of the influence of maximal subgroups of composite index by considering the generalized Frattini subgroup obtained by intersection. For example, if \(\pi\) is a set of primes (with complement \(\pi\) ') then \(S_{\pi}(G)\) is the subgroup of the finite group G obtained by intersecting all maximal M with [G:M] composite and \(\pi\)-free (or G if no such subgroups exist), and \(S_{\pi '}(G)\) is defined analogously. Theorem 5. If G is \(\pi\)- solvable then either \(S_{\pi}(G)\) or \(S_{\pi '}(G)\) is solvable. Other results of a similar nature are obtained.
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 3961939
zbMATH Keywords: maximal subgroups of composite index
zbMATH Keywords: generalized Frattini subgroup
zbMATH Keywords: \(\pi \) -solvable
reviewed by: W. E. Deskins
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90074-5
OpenAlex ID: W2020514679
cites work: Classes of finite groups and their properties
cites work: Q3274985
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cites work: Q5577154
cites work: Endliche Gruppen I
cites work: On the Intersection of a Class of Maximal Subgroups of a Finite Group
cites work: The Influence on a Finite Group of Its Proper Abnormal Structure
description: scientific article; zbMATH DE number 3961939