Scriviamo $[x,y]=[x,{}_{1}y]$ ed $\left[\right[x,{}_{k}y],y]=[x,{}_{k+1}y]$. Cerchiamo gruppi $SL\left(2,q\right)$ con generatori $x,y$ tali che $[x,{}_{m}y]=x$ ed $[y,{}_{n}x]=y$ per alcuni numeri naturali $m$, $n$.

If $𝒳$ is a class of groups, then a group $G$ is said to be minimal non $𝒳$-group if all its proper subgroups are in the class $𝒳$, but $G$ itself is not an $𝒳$-group. The main result of this note is that if $c\>0$ is an integer and if $G$ is a minimal non $\left(\mathrm{ℒℱ}\right)𝒩$ (respectively, $\left(\mathrm{ℒℱ}\right){𝒩}_c$)-group, then $G$ is a finitely generated perfect group which has no non-trivial finite factor and such that $G/Frat\left(G\right)$ is an infinite simple group; where $𝒩$ (respectively, ${𝒩}_c$, $\mathrm{ℒℱ}$) denotes the class of nilpotent (respectively, nilpotent of class at most $c$, locally...