On NR∗ -subgroups of finite groups

Abstract

: Let G be a finite group and let H be a subgroup of G. H is said to be an NR∗ -subgroup of G if there exists a normal subgroup T of G such that G = HT and if whenever K ✁ H and g ∈ G, then Kg ∩ H ∩ T ≤ K . A number of new characterizations of a group G are given, under the assumption that all Sylow subgroups of certain subgroups of G are NR∗ -subgroups.