MATHEMATICS

On $\pi$-supersolvability of finite groups

T. I. Vasilyeva^a, A. G. Koranchuk<sup>b

a</sup> Belarusian State University of Transport, Gomel
^b Francisk Skorina Gomel State University

Abstract: 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.

Keywords: $\pi$-soluble group, $\pi$-supersoluble group, $\mathbb{P}_{\pi}$-subnormal subgroup, normalizers of Sylow subgroups.

UDC: 512.542

Received: 28.01.2023

DOI: 10.54341/20778708_2023_1_54_69