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SOME NEW CHARACTERISATIONS OF FINITE $p$-SUPERSOLUBLE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  08 November 2013

CHANGWEN LI ,
NANYING YANG  and
NA TANG
CHANGWEN LI*
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, PR China
NANYING YANG
Affiliation:
School of Science, Jiangnan University, Wuxi, 214122, PR China
NA TANG
Affiliation:
School of Mathematical Science, Soochow University, Suzhou, 215006,PR China
*
✉[email protected]
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Abstract

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Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be $E$-supplemented in $G$ if there is a subgroup $T$ of $G$ such that $G= HT$ and $H\cap T\leq {H}_{eG} $, where ${H}_{eG} $ denotes the subgroup of $H$ generated by all those subgroups of $H$ which are $S$-quasinormally embedded in $G$. In this paper, some new characterisations of $p$-supersolubility of finite groups are given under the assumption that some primary subgroups are $E$-supplemented.

Keywords

S-quasinormalE-supplementedp-supersolublenilpotent

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 514 - 521
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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