Geodesic
Generalized $\sigma$-subnormal and $\sigma$-permutable subgroups of finite groups
Problemy fiziki, matematiki i tehniki, no. 3 (2021), pp. 76-81

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Throughout the article, all groups are finite and $G$ always denotes a finite group. Moreover, $\sigma$ is some partition of the set of all primes $\mathbb{P}$, i. e. $\sigma=\{\sigma_i\mid i\in I\}$, where $\mathbb{P}=\bigcup_{i\in I}\sigma_i$ and $\sigma_i\cap\sigma_j=\varnothing$ for all $i\ne j$. A $\sigma$-property of a group is any of its properties that do not depend on the choice of the partition $\sigma$ of the set $\mathbb{P}$. This work is devoted to further the study of the $\sigma$-properties of a group. A lot of known results are generalized.
Keywords: finite group, $\sigma$-nilpotent group, $\sigma$-subnormal subgroup, Schmidt group.
Mots-clés : $\sigma$-soluble group 
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     author = {I. N. Safonova and A. N. Skiba},
     title = {Generalized $\sigma$-subnormal and $\sigma$-permutable subgroups of finite groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {76--81},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/PFMT_2021_3_a10/}
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I. N. Safonova; A. N. Skiba. Generalized $\sigma$-subnormal and $\sigma$-permutable subgroups of finite groups. Problemy fiziki, matematiki i tehniki, no. 3 (2021), pp. 76-81. http://geodesic.mathdoc.fr/item/PFMT_2021_3_a10/