On Groups whose Non-Normal Subgroups are either Contranormal or Core-Free

Abstract

A subgroup H of a group G is called contranormal in G if H^G = G. A subgroup H of a group G is called core-free in G if Core_G(H) = . Obviously, these two types of subgroups are the complete opposite of normal subgroups. In this paper, we will obtain the structure of soluble and non-soluble groups whose non-normal subgroups are contranormal. Moreover, we will obtain the structure of some periodic groups whose non-normal subgroups are either contranormal or core-free

Keywords

• contranormal subgroup
• core-free subgroup