NEW CRITERIA FOR p-NILPOTENCE OF FINITE GROUPS

Abstract

A subgroup H is X-g pronormal in G if, for H, X ≤ G and g ∈ G, H ∩ X and Hg ∩ X are conjugate in J = hH ∩ X, Hg ∩ Xi. In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups are X-g pronormal, where X = F(G) is the Fitting subgroup of G.