The influence of weakly pronormal subgroups on the structure of finite groups

Abstract

Let G be a finite group. A subgroup H of G is called pronormal in G if for every $g\in G,$ H and H${}^g$ are conjugate in $<H,H^g>.$ A subgroup H of G is called weakly pronormal in G if there exists a subgroup K of G such that G = HK and $H\cap K$ is pronormal in G. In this paper, we investigate the structure of G under the assumption that some subgroups of G are weakly pronormal in G.

KEYWORD:

• Pronormal subgroups
• saturated formations
• the generalized Fitting subgroup
• weakly pronormal subgroups

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20