Research ArticleNo Access

Finite groups with generalized subnormal and generalized permutable subgroups

Viktoria S. Zakrevskaya

Department of Mathematics and Programming Technology, Francisk Skorina Gomel State University, Gomel 246019, Belarus

E-mail Address: tory.zakreuskaya@gmail.com

https://doi.org/10.1142/S1793557122500164Cited by:0 (Source: Crossref)

Abstract

Let $G$ be a finite group and $A$ a subgroup of $G$ . We say that $A$ is strongly $𝔘$ -subnormal in $G$ if either $A$ is normal in $G$ or $A_{G} \neq A^{G}$ and every chief factor of $G$ between $A_{G}$ and $A^{G}$ is cyclic; strongly $π$ -permutable in $G$ if $A$ permutes with all Hall $π$ ’-subgroups and with all Sylow $p$ -subgroups of $G$ for all $p \in π$ ; partially $π$ -subnormal in $G$ if $A = 〈 L, T 〉$ , where $L$ is a strongly $𝔘$ -subnormal subgroup and $T$ is a $π$ -subnormal subgroup of $G$ . In this paper, we study finite groups whose 3-maximal or 2-maximal subgroups are partially $π$ -subnormal (strongly $π$ -permutable).

Communicated by A. F. Vasilev

Keywords:

AMSC: 20D10, 20D20, 20D30, 20D35

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