  We prove analogs of A.~Selberg's result for finitely generated subgroups of
$\text{Aut}(A)$ and of Engel's theorem for subalgebras of $\text{Der}(A)$ for a
finitely generated associative commutative algebra $A$ over an associative
commutative ring. We prove also an analog of the theorem of W.~Burnside and
I.~Schur about locally finiteness of torsion subgroups of $\text{Aut}(A)$.
