Engel graph associated with a group

2005/10/14 by Alireza Abdollahi, Abdollahi, Alireza
Mathematics · #05C25 #20D60 #20F45 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05C25 #msc:20D60 #msc:20F45

paper · pdf · doi:10.48550/arxiv.math/0510296

Proposition 2.8 is omitted however the proof is correct. Some errors and misprints are corrected. Corollary 2.11 (now Corollary 2.10) is now in a corrected form

arxiv created 2007/08/16 · arxiv updated 2009/12/01

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\backslash L(G) as vertices of E_G and join two distinct vertices x and y whenever [x,_k y]\not=1 and [y,_k x]\not=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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• The Engel graph of almost simple groups
• Engel and co-Engel graphs of finite groups
• The Engel graph of a finite group
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• Engel Elements in Groups