On the right n-Engel group elements

Document Type : Research Paper

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Abstract

In this paper we study right $n$-Engel group elements‎. ‎By modifying a group constructed by Newman and Nickel‎, ‎we construct‎, ‎for each integer $n\geq 5$‎, ‎a 2-generator group $G =\langle a‎, ‎b\rangle$ with the property that $b$ is a right $n$-Engel‎ ‎element but where $[b^k,_n a]$ is of infinite order when $k\notin \{0‎, ‎1\}$‎.

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  • Receive Date: 20 August 2011
  • Revise Date: 14 December 2011
  • Accept Date: 14 December 2011
  • Published Online: 01 March 2012