Abstract
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 E G as follows: Take G \\ L ( G ) as vertices of E G and join two distinct vertices x and y whenever [ x , k y ] ≠ 1 and [ y , k x ] ≠ 1 for all positive integers k. We call E G , the Engel graph of G. In this paper we study the graph theoretical properties of E G .
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