RESEARCH ARTICLE

On the structure of some groups having finite contranormal subgroups

L. A. Kurdachenko^a, N. N. Semko<sup>b

a</sup> Oles Honchar Dnipro National University, Gagarin Avenue 72, 49010, Dnipro, Ukraine
^b Department of Mathematics, University of State Fiscal Service of Ukraine, Universitetska 31, 08205, Irpin, Kyiv Region, Ukraine

Abstract: Following J. S. Rose, a subgroup $H$ of the group $G$ is said to be contranormal in $G$, if $G=H^{G}$. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. We study the structure of Abelian-by-nilpotent groups having a finite proper contranormal $p$-subgroup.

Keywords: contranormal subgroups, Abelian-by-nilpotent groups, hypercenter of a group, $G$-eccentric subgroups, rationally irreducible subgroups.

MSC: 20E99, 20F18, 20F19

Received: 12.11.2020

Language: English

DOI: 10.12958/adm1724