On the right n-Engel group elements

In this paper we study right $n$-Engel group elements‎. ‎By modifying a group constructed by Newman and Nickel‎, ‎we construct‎, ‎for each integer $n\geq ۵$‎, ‎a ۲-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 $k\notin \{۰‎, ‎۱\}$‎.

Keywords:

Engel elements , right Engel elements , right n-Engel elements