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Mat. Zametki, 2015, Volume 98, Issue 2, Pages 180–186 (Mi mz10625)  

An Example of a Nonlinearizable Quasicyclic Subgroup in the Automorphism Group of the Polynomial Algebra

V. G. Bardakovabc, M. V. Neshchadimab

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Chelyabinsk State University

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00513
13-01-92697-ИНД_а
14-01-00014
Ministry of Education and Science of the Russian Federation 14.Z50.31.0020
This work was supported by the Russian Foundation for Basic Research (grants nos. 13-01-00513, 13-01-92697-IND-a, and 14-01-00014) and also by the Laboratory of Quantum Topology of the Chelyabinsk State University (grant of the Government of the Russian Federation no. 14. Z50.31.0020).


DOI: https://doi.org/10.4213/mzm10625

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English version:
Mathematical Notes, 2015, 98:2, 210–215

Bibliographic databases:

Document Type: Article
UDC: 512.7
Received: 02.10.2014
Revised: 16.12.2014

Citation: V. G. Bardakov, M. V. Neshchadim, “An Example of a Nonlinearizable Quasicyclic Subgroup in the Automorphism Group of the Polynomial Algebra”, Mat. Zametki, 98:2 (2015), 180–186; Math. Notes, 98:2 (2015), 210–215

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