Groups with an Engel restriction on proper subgroups of infinite rank-Reference-Cited by-同舟云学术

Groups with an Engel restriction on proper subgroups of infinite rank

Published:2019-10-29 Issue:11 Volume:19 Page:2050213
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Abdollahi Alireza¹²,Trabelsi Nadir³,Zitouni Amel³

Affiliation:

1. Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran

2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

3. Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, University Ferhat Abbas Setif 1, Setif 19000, Algeria

Abstract

We prove that a locally graded group whose proper subgroups are Engel (respectively, [Formula: see text]-Engel) is either Engel (respectively, [Formula: see text]-Engel) or finite. We also prove that a group of infinite rank whose proper subgroups of infinite rank are Engel (respectively, [Formula: see text]-Engel) is itself Engel (respectively, [Formula: see text]-Engel), provided that [Formula: see text] belongs to the Černikov class [Formula: see text], which is the closure of the class of periodic locally graded groups by the closure operations Ṕ, P̀, R and L.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498820502138

Reference13 articles.

1. On Minimal Non-Baer-Groups

2. Groups with restricted non-normal subgroups

3. Theorem on groups of finite special rank

4. Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank

5. Groups with restrictions on subgroups of infinite rank

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