A generalization of the malnormal subgroups

1Kurdachenko, LA, 2Semko, NN, 3Subbotin, IYa.
1Oles Honchar Dnipropetrovsk National University
2State Tax Service National University of Ukraine, Irpin
3National University, Los Angeles, USA
Dopov. Nac. akad. nauk Ukr. 2019, 3:25-28
https://doi.org/10.15407/dopovidi2019.03.025
Section: Mathematics
Language: English
Abstract: 

A subgroup H of a group G is called malonormal in G, if H Hx = ‹1› for every element x NG(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: Frobenius group, generalized radical groups, locally graded groups, malnormal subgroups, malonormal subgroups
References: 

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