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Theses

Automorphismes extérieurs du groupe de Burnside libre

Abstract : The free Burnside group of exponent n, B(r,n), is the quotient of the free group of rank r by the subgroup generated by all n-th powers. This group was introduced in 1902 by W. Burnside who asked wether it has to be finite or not. Since the work of P.S. Novikov and S.I. Adian in the late sixties, it is knows that for exponent n large enough the answer is no. In this thesis, we are interested in the outer automorphisms of B(r,n). Using the geometrical point of view on small cancellation theory developed by T. Delzant and M. Gromov, we provide a large class of automorphisms of the free group that induces infinite order elements of Out(B(r,n)). Moreover we proved that Out(B(r,n)) contains free and free abelian subgroups.
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Submitted on : Friday, June 4, 2010 - 2:00:25 PM
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Rémi Coulon. Automorphismes extérieurs du groupe de Burnside libre. Mathématiques [math]. Université de Strasbourg, 2010. Français. ⟨NNT : 2010STRA6057⟩. ⟨tel-00489295⟩

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