On the structure of some locally nilpotent groups without contranormal subgroups

Author:

Kurdachenko Leonid A.1,Longobardi Patrizia2,Maj Mercede2

Affiliation:

1. Department of Algebra and Geometry , School of Mathematics and Mechanics , University of Dnipro , Gagarin prospect 72 , Dnipro 10, 49010 , Ukraine

2. Dipartimento di Matematica , Università di Salerno , via Giovanni Paolo II, 132, 84084 Fisciano (Salerno) , Italy

Abstract

Abstract Following J. S. Rose, a subgroup 𝐻 of a group 𝐺 is said to be contranormal in 𝐺 if G = H G G=H^{G} . It is well known that a finite group is nilpotent if and only if it has no proper contranormal subgroups. We study nilpotent-by-Černikov groups with no proper contranormal subgroups. Furthermore, we study the structure of groups with a finite proper contranormal subgroup.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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