On \(\pi\)-quasinormal subgroups in finite groups
type: Item
instance of: scholarly article
title: On \(\pi\)-quasinormal subgroups in finite groups
zbMATH Open document ID: 0681.20013
DOI: 10.1007/BF01277055
author: Péter Z. Hermann
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: This is basically a continuation of earlier work by the author, K. Corradi and L. Hethelyi; two theorems are proved. Theorem 1. If A and B are \(\pi\)-quasinormal subgroups of finite group G (for some set \(\pi\) of primes), if \(G=AB\), and if A and B are \(\pi\)-separable, then G is also \(\pi\)-separable. Theorem 2. If A and B are q-quasinormal subgroups of finite group G, if \(G=AB\), and if A and B are in N(p,q) then G is also in N(p,q). Here N(p,q), for distinct primes p and q, denotes the class of finite groups in which a p-subgroup is normalized by a q-subgroup exactly when it is centralized by it. There are additional results, such as Lemma 5. If A and B are \(\pi\)-quasinormal subgroups of finite group G with \(AB=BA\) then \(A\cap B\) is also \(\pi\)-quasinormal in G.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D35
zbMATH DE Number: 4114869
zbMATH Keywords: factorizable groups
zbMATH Keywords: \(\pi\)-quasinormal subgroups
zbMATH Keywords: \(\pi\)-separable
zbMATH Keywords: finite groups
reviewed by: W. E. Deskins
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01277055
OpenAlex ID: W1982015186
description: scientific article; zbMATH DE number 4114869