Finite Groups Whose Minimal Subgroups are Weakly -SUBGROUPS (original) (raw)

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩H g ≤ H for all g ∈ G. A subgroup H of G is called a weakly H *-subgroup in G if there exists a subgroup K of G such that G = HK and H ∩ K is an H-subgroup in G. We investigate the structure of the finite group G under the assumption that every cyclic subgroup of G of prime order p or of order 4 (if p = 2) is a weakly H *-subgroup in G. Our results improve and extend a series of recent results in the literature. following concept: A subgroup H of a group G is called c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ H G. Also, in 2000, Bianchi et al. [4] introduced the concept of an H-subgroup as follows: A subgroup H of a group G is called an H-subgroup if N G (H) ∩ H g ≤ H for all g ∈ G. Recently, in 2012, Asaad, Heliel and Al-Shomrani [2] introduced a new concept, called a weakly H-subgroup, as follows: A subgroup H of a group G is called a weakly H-subgroup in G if there