Year: 2011
Author: Junxin Wang
Communications in Mathematical Research , Vol. 27 (2011), Iss. 4 : pp. 360–368
Abstract
A finite group $G$ is called a generalized $PST$-group if every subgroup contained in $F(G)$ permutes all Sylow subgroups of $G$, where $F(G)$ is the Fitting subgroup of $G.$ The class of generalized $PST$-groups is not subgroup and quotient group closed, and it properly contains the class of $PST$-groups. In this paper, the structure of generalized $PST$-groups is first investigated. Then, with its help, groups whose every subgroup (or every quotient group) is a generalized $PST$-group are determined, and it is shown that such groups are precisely $PST$-groups. As applications, $T$-groups and $PT$-groups are characterized.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-CMR-19078
Communications in Mathematical Research , Vol. 27 (2011), Iss. 4 : pp. 360–368
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: $s$-permutable subgroup power automorphism $PST$-group.