On the structure of some locally nilpotent groups without contranormal subgroups-Reference-Cited by-同舟云学术

On the structure of some locally nilpotent groups without contranormal subgroups

Published:2021-06-30 Issue:1 Volume:25 Page:75-90
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

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

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2021-0024/pdf

Reference20 articles.

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4. S. N. Černikov, Groups with prescribed properties for systems of infinite subgroups, Ukrain. Mat. Ž. 19 (1967), 111–131.

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