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April  2007, 17(2): 423-439. doi: 10.3934/dcds.2007.17.423

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, Brazil
2. 

Dept. de Matematica, CCE UEL, Campus Universitario, Caixa, Postal 6001 Londrina PR CEP 86051-990, Brazil

Received  December 2005 Revised  September 2006 Published  November 2006

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, 37C5.
Citation: Julio C. Rebelo, Ana L. Silva. On the Burnside problem in Diff(M). Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 423-439. doi: 10.3934/dcds.2007.17.423
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