%0 Journal Article
%T On weakly $SS$-quasinormal and hypercyclically embedded properties of finite groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Zhao, Tao
%D 2014
%\ 12/01/2014
%V 3
%N 4
%P 17-25
%! On weakly $SS$-quasinormal and hypercyclically embedded properties of finite groups
%K $s$-permutable
%K weakly $SS$-quasinormal
%K $p$-nilpotent
%K hypercyclically embedded
%R 10.22108/ijgt.2014.4950
%X A subgroup $H$ is said to be $s$-permutable in a group $G$, if $HP=PH$ holds for every Sylow subgroup $P$ of $G$. If there exists a subgroup $B$ of $G$ such that $HB=G$ and $H$ permutes with every Sylow subgroup of $B$, then $H$ is said to be $SS$-quasinormal in $G$. In this paper, we say that $H$ is a weakly $SS$-quasinormal subgroup of $G$, if there is a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable and $H\cap T$ is $SS$-quasinormal in $G$. By assuming that some subgroups of $G$ with prime power order have the weakly $SS$-quasinormal properties, we get some new characterizations about the hypercyclically embedded subgroups of $G$. A series of known results in the literature are unified and generalized.
%U https://ijgt.ui.ac.ir/article_4950_c0915a41877e3a4bb1db406fbaca42cf.pdf