Geodesic
On $\pi$-supersolvability of finite groups
Problemy fiziki, matematiki i tehniki, no. 1 (2023), pp. 69-74

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A subgroup $H$ of a group $G$ is called $\mathbb{P}_{\pi}$-subnormal in $G$ if either $H=G$ or from $H$ to $G$ there exists a chain of subgroups, whose every index is either a prime in $\pi$ or a $\pi'$-number ($\pi$ is some set of primes). For a finite $\pi$-closed group with given $\mathbb{P}_{\pi}$-subnormal subgroups, the necessary and sufficient conditions of $\pi$-supersolvability are obtained.
Mots-clés : $\pi$-soluble group
Keywords: $\pi$-supersoluble group, $\mathbb{P}_{\pi}$-subnormal subgroup, normalizers of Sylow subgroups. 
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     title = {On $\pi$-supersolvability of finite groups},
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T. I. Vasilyeva; A. G. Koranchuk. On $\pi$-supersolvability of finite groups. Problemy fiziki, matematiki i tehniki, no. 1 (2023), pp. 69-74. http://geodesic.mathdoc.fr/item/PFMT_2023_1_a10/