Abstract:
Let $\{\sigma_i \mid i\in I\}$ be some partition of the set of all primes $\mathbb{P}$ and let $G$ be a finite group. $G$ is said to be $\sigma$-full if $G$ has a Hall $\sigma_i$-subgroup for all $i$. A subgroup $A$ of $G$ is said to be $\sigma$-permutable in $G$ if $G$ is $\sigma$-full and $A$ permutes with all Hall $\sigma_i$-subgroups $H$ of $G$ (that is, $AH=HA$) for all $i$. In this paper, we give a survey of some recent results on $\sigma$-permutable subgroups of finite groups.
Keywords:finite group, a Robinson $\sigma$-complex of a group, $\sigma$-permutable subgroup, $\sigma$-soluble group, $\sigma$-supersoluble group, $\sigma$-CS-group.
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