  It is well known that every finite subgroup of automorphism group of
polynomial algebra of rank 2 over the field of zero characteristic is
conjugated with a subgroup of linear automorphisms. We prove that it is not
true for an arbitrary torsion subgroup. We construct an example of abelian
$p$-group of automorphism of polynomial algebra of rank 2 over the field of
complex numbers, which is not conjugated with a subgroup of linear
automorphisms.
