On minimal subgroups of finite groups
type: Item
instance of: scholarly article
title: On minimal subgroups of finite groups
zbMATH Open document ID: 0930.20021
DOI: 10.1007/BF00052909
author: M. C. Pedreza-Aguilera
author: Adolfo Ballester-Bolinches
published in: Acta Mathematica Hungarica
publication date: 1999-10-31T00:00:00Z
review text: All groups considered in this paper are finite. Recall that a minimal subgroup of a group is a subgroup of prime order. Recently there has been a considerable interest to study the structure of a group \(G\) under the assumption that all minimal subgroups of \(G\) are well-situated in the group. Ito proved that if the center of a finite group \(G\) of odd order contains all minimal subgroups, then \(G\) is nilpotent. The present paper represents an attempt to extend and improve the results of Ito and some other authors through the theory of formations.
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 1354956
zbMATH Keywords: minimal subgroups
zbMATH Keywords: formations
zbMATH Keywords: finite groups
MaRDI profile type: Publication
cites work: On the solvability of finite groups
cites work: \({\mathfrak h}\)-normalizers and local definitions of saturated formations of finite groups
cites work: Finite groups whose minimal subgroups are normal
cites work: The influence of minimal p-subgroups on the structure of finite groups
cites work: Finite soluble groups
cites work: Endliche Gruppen I
cites work: Finite solvable groups whose \(\mathfrak F\)-hypercenter contains all minimal subgroups
cites work: Finite solvable groups whose \(\mathfrak F\)-hypercenter contains all minimal subgroups. II
full work available at URL: https://doi.org/10.1007/bf00052909
OpenAlex ID: W1972845428
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description: scientific article; zbMATH DE number 1354956