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Paper IPM / M / 8722  


Abstract:  
Let G be a nonEngel 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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