Abstract
It is still an open question whether a left 3Engel element of a group G is always contained in the Hirsch–Plotkin radical of G. In this paper we begin a systematic study of this problem. The problem is first rephrased as saying that a certain type of groups are locally nilpotent. We refer to these groups as sandwich groups as they can be seen as the analogs of sandwich algebras in the context of Lie algebras. We show that any 3generator sandwich group is nilpotent and obtain a powerconjugation presentation for the free 3generator sandwich group. As an application we show that the left 3Engel elements in any group G of exponent 5 are in the Hirsch–Plotkin radical of G.
Original language  English 

Pages (fromto)  4171 
Number of pages  31 
Journal  Journal of Algebra 
Volume  414 
Early online date  9 Jun 2014 
DOIs  
Publication status  Published  15 Sep 2014 
Keywords
 Engel elements
 groups of exponent 5
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Gunnar Traustason
 Department of Mathematical Sciences  Deputy Head of Department
Person: Research & Teaching