Small doubling in $m$-Engel groups

Abstract

We study some inverse problems of small doubling type in the class of $m$-Engel groups‎. ‎In particular we investigate the structure of a finite subset $S$ of a torsion-free $m$-Engel group if $|S^2| = 2|S|+b$‎, ‎where $0 leq b leq |S|-4$‎, ‎for some values of $b$‎.