On some generalization of the malnormal subgroups

‎‎A subgroup $H$ of a group $G$ is called malonormal in $G$ if $H \cap H^x =\langle ۱\rangle$ for every element $x \notin N_G(H)$‎. ‎These subgroups are generalizations of malnormal subgroups‎. ‎Every malnormal subgroup is malonormal‎, ‎and every selfnormalizing malonormal subgroup is malnormal‎. ‎Furthermore‎, ‎every normal subgroup is malonormal‎. ‎In this paper we obtain a description of finite and certain infinite groups‎, ‎whose subgroups are malonormal‎.

Keywords:

‎‎Malnormal Subgroups‎ , ‎Malonormal Subgroups‎ , ‎Frobenius Group‎ , ‎Locally Graded groups‎ , ‎Generalized Radical Groups