Finite Groups Whose Minimal Subgroups are Weakly -SUBGROUPS

Let G be a finite group. A subgroup H of G is called an -subgroup in G if NG(H)∩Hg ≤ H for all g ∈ G. A subgroup H of G is called a weakly -subgroup in G if there exists a normal subgroup K of G such that G = HK and H∩K is an -subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly -subgroup in G. Our results improve and generalize several recent results in the literature.