# On some generalization of the malnormal subgroups

Document Type: Ischia Group Theory 2018

Authors

1 National University of Dnipro

2 University of State Fiscal Service of Ukraine

3 Department of Mathematics and Natural Sciences, College of Letters and Sciences, National University, USA

Abstract

‎‎A subgroup $H$ of a group $G$ is called malonormal in $G$ if $H \cap H^x =\langle 1\rangle$ 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.

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