On the normal index of maximal subgroups in finite groups
type: Item
instance of: scholarly article
title: On the normal index of maximal subgroups in finite groups
zbMATH Open document ID: 0699.20016
DOI: 10.1016/0022-4049(90)90150-G
author: Adolfo Ballester-Bolinches
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: The author uses results from primitive group theory to generalize some work of Beidleman and Spencer, Mukherjee, and Mukherjee and Bhattacharya on criteria for solvability, supersolvability, and nilpotency to \(\Pi\)- solvability, \(\Pi\)-supersolvability, and \(\Pi\)-nilpotency. Typical is Theorem 1: Let \(\Pi\) be a set of primes. If finite group G has a \(\Pi\)- solvable maximal subgroup M whose normal index equals its index in G, then G is \(\Pi\)-solvable.
reviewed by: W. E. Deskins
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 4146239
zbMATH Keywords: \(\Pi \) -solvability
zbMATH Keywords: \(\Pi \) -supersolvability
zbMATH Keywords: \(\Pi \) -nilpotency
zbMATH Keywords: \(\Pi \) -solvable maximal subgroup
zbMATH Keywords: normal index
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4146239