The influence of weakly pronormal subgroups on the supersolvability of finite groups.

Let G be a finite group and H a subgroup of G. We say that H is pronormal in G if for every g ∈ G , the subgroups H and H g are conjugate in ⟨ H , H g ⟩ ; H is called weakly pronormal in G if there exists a subgroup K of G such that G = HK and H ∩ K is pronormal in G. In this paper, we investigate the structure of G under the assumption that certain subgroups of G are weakly pronormal in G. Our results improve and generalize new recent results in the literature. [ABSTRACT FROM AUTHOR]