On $\Pi$-property of $p$-subgroups and the $p$-supersolvability of Finite Groups
Abstract
A subgroup $H$ of a group $G$ is said to satisfy $\Pi$-property in $G$ such that for any $G$-chief factor $U/V$, $|G/V:N_{G/V}(HV/V\cap U/V)|$ is a $\pi(HV/V\cap U/V)$-number. In this paper, we present a new criterion for $p$-supersolvability of finite groups by using of a small quantity of maximal subgroups of a Sylow $p$-subgroup satisfying the $\Pi$-property. As applications, we obtain some sufficient conditions for a finite group to be $p$-nilpotent and supersolvable. A number of known results are improved and extended.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Topics in Algebra
Rings
Modules
and Algebras
Publication details
- Journal / source
- European Journal of Pure and Applied Mathematics
- Volume
- 19
- Issue
- 1
- Pages
- 6616–6616
- Publication date
- 16 February 2026
- Language
- EN