Geodesic
An Example of a Nonlinearizable Quasicyclic Subgroup in the Automorphism Group of the Polynomial Algebra
Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 180-186

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As is well known, every finite subgroup of the automorphism group of the polynomial algebra of rank two over a field of characteristic zero is conjugate to the subgroup of linear automorphisms. We show that this can fail for an arbitrary periodic subgroup. We construct an example of an Abelian $p$-subgroup of the automorphism group of the polynomial algebra of rank two over the field of complex numbers which is not conjugate to any subgroup of linear automorphisms.
Keywords: polynomial algebra of rank two, linear automorphism, $p$-subgroup, quasicyclic subgroup, algebra of formal power series. 
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     author = {V. G. Bardakov and M. V. Neshchadim},
     title = {An {Example} of a {Nonlinearizable} {Quasicyclic} {Subgroup} in the {Automorphism} {Group} of the {Polynomial} {Algebra}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {180--186},
     publisher = {mathdoc},
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     number = {2},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a2/}
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V. G. Bardakov; M. V. Neshchadim. An Example of a Nonlinearizable Quasicyclic Subgroup in the Automorphism Group of the Polynomial Algebra. Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 180-186. http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a2/