A complete classification of minimal non-PS-groups

Pengfei GUO; Junxin WANG; Hailiang ZHANG

doi:10.1007/s12044-014-0195-2

A complete classification of minimal non-PS-groups

Pengfei GUO, Junxin WANG, Hailiang ZHANG^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

Abstract

Let G be a finite group. A subgroup H of G is called s-permutable in G if it permutes with every Sylow subgroup of G, and G is called a PS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-permutable in G. In this paper, we give a complete classification of finite groups which are not PS-groups but their proper subgroups are all PS-groups.

Original language	English
Pages (from-to)	511-516
Number of pages	6
Journal	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume	124
Issue number	4
DOIs	https://doi.org/10.1007/s12044-014-0195-2
Publication status	Published - Nov 2014

Research Keywords

Minimal non-PS-groups
Power automorphisms
PS-groups
Supersolvable groups

Access Output

10.1007/s12044-014-0195-2

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{bc45f98a0c874c86a24cb115682b5a85,

title = "A complete classification of minimal non-PS-groups",

abstract = "Let G be a finite group. A subgroup H of G is called s-permutable in G if it permutes with every Sylow subgroup of G, and G is called a PS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-permutable in G. In this paper, we give a complete classification of finite groups which are not PS-groups but their proper subgroups are all PS-groups.",

keywords = "Minimal non-PS-groups, Power automorphisms, PS-groups, Supersolvable groups",

author = "Pengfei GUO and Junxin WANG and Hailiang ZHANG",

year = "2014",

month = nov,

doi = "10.1007/s12044-014-0195-2",

language = "English",

volume = "124",

pages = "511--516",

journal = "Proceedings of the Indian Academy of Sciences: Mathematical Sciences",

issn = "0253-4142",

publisher = "Indian Academy of Sciences",

number = "4",

}

TY - JOUR

T1 - A complete classification of minimal non-PS-groups

AU - GUO, Pengfei

AU - WANG, Junxin

AU - ZHANG, Hailiang

PY - 2014/11

Y1 - 2014/11

N2 - Let G be a finite group. A subgroup H of G is called s-permutable in G if it permutes with every Sylow subgroup of G, and G is called a PS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-permutable in G. In this paper, we give a complete classification of finite groups which are not PS-groups but their proper subgroups are all PS-groups.

AB - Let G be a finite group. A subgroup H of G is called s-permutable in G if it permutes with every Sylow subgroup of G, and G is called a PS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-permutable in G. In this paper, we give a complete classification of finite groups which are not PS-groups but their proper subgroups are all PS-groups.

KW - Minimal non-PS-groups

KW - Power automorphisms

KW - PS-groups

KW - Supersolvable groups

UR - http://www.scopus.com/inward/record.url?scp=84924258555&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84924258555&origin=recordpage

U2 - 10.1007/s12044-014-0195-2

DO - 10.1007/s12044-014-0195-2

M3 - RGC 21 - Publication in refereed journal

AN - SCOPUS:84924258555

SN - 0253-4142

VL - 124

SP - 511

EP - 516

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

IS - 4

ER -

A complete classification of minimal non-PS-groups

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this