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

2015/01/12 by Bardakov, Valeriy G., Neshchadim, Mikhail V.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1501.02626

Abstract

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.

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