On the Burnside problem in  Diff(M)

Julio C. Rebelo; Ana L. Silva

doi:10.3934/dcds.2007.17.423

Article Contents

2007, Volume 17, Issue 2: 423-439. Doi: 10.3934/dcds.2007.17.423

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On the Burnside problem in Diff(M)

Julio C. Rebelo^1, and
Ana L. Silva^2,

1.
Dept. de Matematica, PUC-Rio, R. Marques de S. Vicente 225, Rio de Janeiro RJ CEP 22453-900
2.
Dept. de Matematica, CCE UEL, Campus Universitario, Caixa, Postal 6001 Londrina PR CEP 86051-990

Received: November 30, 2005

Revised: August 31, 2006

Published: April 2007

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Abstract

In this paper we obtain some non-linear analogues of Schur's theorem asserting that a finitely generated subgroup of a linear group all of whose elements have finite order is, in fact, finite. The main result concerns groups of symplectomorphisms of certain manifolds of dimension $4$ including the torus $T^4$.

Keywords:

Burnside problem.

Mathematics Subject Classification: 53D25, 37C50.

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