On the structure of groups, whose subgroups are either normal or core-free

1Kurdachenko, LA
1Pypka, AA
2Subbotin, IYa.
1Oles Honchar Dnipropetrovsk National University
2National University, Los Angeles, USA
Dopov. Nac. akad. nauk Ukr. 2019, 4:17-20
Section: Mathematics
Language: English

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

Keywords: core-free subgroup, Dedekind group, normal subgroup

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