| Title | On groups, whose non-normal subgroups are either contranormal or core-free |
| Publication Type | Journal Article |
| Year of Publication | 2020 |
| Authors | Kurdachenko, LA, Pypka, AA, Subbotin, IYa. |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2020.10.003 |
| Issue | 10 |
| Section | Mathematics |
| Pagination | 3-8 |
| Date Published | 10/2020 |
| Language | English |
| Abstract | 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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