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

Example of non-linearizable quasi-cyclic subgroup of automorphism group of polynomial algebra