Engel graph associated with a group

[摘要] Let G be a non-Engel group and let L(G) be the set of all left Engel elements of G. Associate with G a graph epsilon(G) as follows: Take G\L(G) as vertices of epsilon(G) and join two distinct vertices x and y whenever [x,(k) y] not equal 1 and [y,(k) x] not equal 1 for all positive integers k. We call epsilon(G), the Engel graph of G. In this paper we study the graph theoretical properties of epsilon(G) (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] left Engel elements;Engel groups;nilpotent groups