Table of Contents
Algebra
Volume 2013, Article ID 153691, 5 pages
http://dx.doi.org/10.1155/2013/153691
Research Article

Finite Groups with Some -Supplemented Subgroups

1School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi 530023, China
2College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
3School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received 30 March 2013; Accepted 29 May 2013

Academic Editor: Antonio M. Cegarra

Copyright © 2013 Guo Zhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a subgroup of a finite group , a prime dividing the order of , and a Sylow -subgroup of for prime We say that is -supplemented in if there is a subgroup of such that and where denotes the subgroup of generated by all those subgroups of which are -quasinormally embedded in In this paper, we characterize -nilpotency and supersolvability of under the assumption that all maximal subgroups of are -supplemented in .