Type: Article
Groups with an Engel restriction on proper subgroups of infinite rank
Journal: Journal of Algebra and its Applications (17936829)Year: 1 November 2020Volume: 19Issue:
DOI:10.1142/S0219498820502138Language: English
Abstract
We prove that a locally graded group whose proper subgroups are Engel (respectively, k-Engel) is either Engel (respectively, k-Engel) or finite. We also prove that a group of infinite rank whose proper subgroups of infinite rank are Engel (respectively, k-Engel) is itself Engel (respectively, k-Engel), provided that G belongs to the ernikov class , which is the closure of the class of periodic locally graded groups by the closure operations Ṕ, P`, R and L. © 2020 World Scientific Publishing Company.
Author Keywords
Engellocally (soluble-by-finite)Prüfer rank