Advanced Search

We use notations: $[x,y]=[x_{,1}y]$ and $[x_{,k+1}y]$ e $[[x_{,k}y],y]$. We consider groups generated by $x$, $y$ satisfying relations $x=[x_{,n}y],y=[y_{,n}x]$ or $[x,y]=[x_{,n}y]$, $[y,x]=[y_{,n}x]$. We call groups of the first type mep-groups and of the second type nmep-groups. We show many properties and examples of mep- and nmep-groups. We prove that if $p$ is a prime then the group $S{l}_2(p)$ is a nmep-group. We give the necessary and sufficient conditions for metacyclic group to be a nmep-group and we show that nmep-groups with presentation $⟨x,y\mid [x,y]=[x_{,2}y],[y,x]=[y_{,2}x],x^n,y^m⟩$ are finite.