Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T21:54:09.404Z Has data issue: false hasContentIssue false
  • English
  • Français

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
*
✉lcw2000@126.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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. 

References

Ballester-Bolinches, A. and Pedraza-Aguilera, M. C., ‘Sufficient conditions for supersolvability of finite groups’, J. Pure Appl. Algebra 127 (1998), 113–118.Google Scholar
Kegel, O. H., ‘Sylow–Gruppen and subnormalteiler endlicher Gruppen’, Math. Z. 78 (1962), 205–221.CrossRefGoogle Scholar
Gorenstein, D., Finite Groups (Harper and Row, New York, 1968).Google Scholar
Guo, W., The Theory of Classes of Groups (Science Press-Kluwer Academic Publishers, Beijing, 2000).Google Scholar
Huppert, B., Endliche Gruppen I (Springer, Berlin–New York, 1967).CrossRefGoogle Scholar
Li, C., ‘A note on a result of Skiba’, J. Group Theory 15 (2012), 385–396.CrossRefGoogle Scholar
Li, D. and Guo, X., ‘The influence of $c$-normality of subgroups on the structure of finite groups’, J. Pure Appl. Algebra 150 (2000), 53–60.Google Scholar
Li, Y., Wang, Y. and Wei, H., ‘On $p$-nilpotency of finite groups with some subgroups $\pi $-quasinormally embedded’, Acta Math. Hungar. 108 (2005), 283–298.CrossRefGoogle Scholar
Robinson, D. J. S., A Course in Theory of Groups (Springer, New York–Heidelberg–Berlin, 1982).Google Scholar
Schmidt, P., ‘Subgroups permutable with all Sylow subgroups’, J. Algebra 207 (1998), 285–293.CrossRefGoogle Scholar
Skiba, A. N., ‘On weakly $S$-permutable subgroups of finite groups’, J. Algebra 315 (2007), 192–209.Google Scholar
Wang, Y., Wei, H. and Li, Y., ‘A generalization of Kramer’s theorem and its application’, Bull. Aust. Math. Soc. 65 (2002), 467–475.CrossRefGoogle Scholar
Yang, N., Guo, W. and Shemetkova, O. L., ‘Finite groups with $S$-supplemented $p$-subgroups’, Siberian Math. J. 53 (2012), 371–376.CrossRefGoogle Scholar