On groups, whose non-normal subgroups are either contranormal or core-free

1Kurdachenko, LA
1Pypka, AA
2Subbotin, IYa.
1Oles Honchar Dnipropetrovsk National University
2National University, Los Angeles, USA
Dopov. Nac. akad. nauk Ukr. 2020, 10:3-8
Section: Mathematics
Language: English

We investigate the influence of some natural types of subgroups on the structure of groups. A subgroup H of a group G is called contranormal in G, if G = HG. A subgroup H of a group G is called core-free in G, if CoreG(H) = 〈1〉. We study the groups, in which every non-normal subgroup is either contranormal or core-free. In particular, we obtain the structure of some monolithic and non-monolithic groups with this property.

Keywords: contranormal subgroup, core-free subgroup, monolithic group, normal subgroup

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