ON THE SUBNORMALISER CONDITION FOR SUBGROUPS

Abstract

A subgroup H of G is said to satisfy the subnormaliser condition in G if for every subgroup K of G such that H K, then NG(K) ≤ NG(H). In this paper, we study this embedding property of subgroups. We establish the relation between groups, whose subgroups satisfy the subnormaliser condition and the so called T-groups, i.e., the groups, in which the normality is a transitive relation.