S. F. Kamornikov, V. N. Tyutyanov, “A criterion for the $\sigma$-subnormality of a subgroup in a finite $3'$-group”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, Number 8,Pages 36

This article is cited in 4 papers

A criterion for the $\sigma$-subnormality of a subgroup in a finite $3'$-group

S. F. Kamornikov^a, V. N. Tyutyanov^b

^a Francisk Skorina Gomel State University, 104 Sovetskaya str., Gomel, 246019 Republic of Belarus
^b Gomel Branch of the International University , 46 а October Ave., Gomel, 246029 Republic of Belarus

Abstract: For a partition $\sigma$ of the set $\mathbb{P}$ of all primes, it is solved, that if a subgroup $H$ of a finite $3'$-group $G$ is $\sigma$-subnormal in $<H,H^x>$ for any $x \in G$, then $H$ is $\sigma$-subnormal in $G$.

Keywords: finite group, $\sigma$-subnormal subgroup, subnormal subgroup, Suzuki group.

UDC: 512.542

Received: 23.09.2019
Revised: 23.09.2019
Accepted: 29.06.2020

DOI: 10.26907/0021-3446-2020-8-36-43