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 ...

Let $gamma_n=[x_1,ldots,x_n]$ be the $n$th lower central word‎. ‎Suppose that $G$ is a profinite group‎ ‎where the conjugacy classes $x^{gamma_n(G)}$ contains less than $2^{aleph_0}$‎ ‎elements‎ ‎for any $x in G$‎. ‎We ...

An automorphism $alpha$ of the group $G$ is said to be $n$-unipotent if $[g,_nalpha]=1$ for all $gin G$‎. ‎In this paper we obtain some results related to nilpotency of groups of $n$-unipotent automorphisms of solvable ...

Here is list of open problems from the conference Engel Type Conditions in Groups in Bath that was held in April 2019.

‎The theory of Engel groups plays an important role in group theory since these groups are closely related to the Burnside problems‎. ‎In this survey we consider several classical and novel algorithmic problems for Engel ...