Geodesic
Criteria for $\pi$-separability of a finite group
Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 81-84.

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Throughout this paper all groups are finite and $G$ always denotes a finite group. The group $G$ is said to be $\pi$-separable if every chief factor of $G$ is either a $\pi$-group or a $\pi'$-group. A subgroup $A$ of $G$ is said to be $\pi,\pi'$-subnormal in $G$ if there is a subgroup chain $A=A_0\leqslant A_1\leqslant\dots\leqslant A_n=G$ such that either $A_{i-1}\trianglelefteq A_i$ or $A_i/(A_{i-1})_{A_i}$ is a $\pi$-separable group for all $i = 1, \dots, n$. In this paper we study the influence of $\pi,\pi'$-subnormal subgroups on the structure of the group.
Keywords: finite group, $\pi$-separable group, $\pi,\pi'$-subnormal subgroup, Hall subgroup. 
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I. M. Dergacheva; I. P. Shabalina; E. A. Zadorozhnyuk. Criteria for $\pi$-separability of a finite group. Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 81-84. http://geodesic.mathdoc.fr/item/PFMT_2021_4_a12/

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