Geodesic
On $\sigma$-permutable subgroups of finite groups
Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 61-65

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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, $\sigma$-supersoluble group
Mots-clés : $\sigma$-soluble group, $\sigma$-CS-group. 
@article{PFMT_2017_3_a10,
     author = {V. M. Selkin and A. N. Skiba},
     title = {On $\sigma$-permutable subgroups of finite groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {61--65},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2017_3_a10/}
}
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V. M. Selkin; A. N. Skiba. On $\sigma$-permutable subgroups of finite groups. Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 61-65. http://geodesic.mathdoc.fr/item/PFMT_2017_3_a10/