Volume 27, Issue 4
On Generalized $PST$-Groups

Commun. Math. Res., 27 (2011), pp. 360-368.

Published online: 2021-05

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• 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.

• Keywords

$s$-permutable subgroup, power automorphism, $PST$-group.

20D10, 20D20

• BibTex
• RIS
• TXT
@Article{CMR-27-360, author = {Junxin and Wang and and 18427 and and Junxin Wang}, title = {On Generalized $PST$-Groups}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {4}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19078.html} }
TY - JOUR T1 - On Generalized $PST$-Groups AU - Wang , Junxin JO - Communications in Mathematical Research VL - 4 SP - 360 EP - 368 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19078.html KW - $s$-permutable subgroup, power automorphism, $PST$-group. AB -

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.

Junxin Wang. (2021). On Generalized $PST$-Groups. Communications in Mathematical Research . 27 (4). 360-368. doi:
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