Given a field K of characteristic p > 2 and a finite group G, necessary and sufficient conditions for the unit group U(KG) of the group algebra KG to be centrally metabelian are obtained. It is observed that U(KG) is centrally metabelian if and only if KG is Lie centrally metabelian.

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 $m$, $n$.