Embedding free Burnside groups in finitely presented groups

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We construct an embedding of a free Burnside group B(m,n) of odd n > 2⁴⁸ and rank m >1 in a finitely presented group with some special properties. The main application of this embedding is an easy construction of finitely presented non-amenable groups without noncyclic free subgroups (which provides a finitely presented counterexample to the von Neumann problem on amenable groups). As another application, we construct weakly finitely presented groups of odd exponent n ≫ 1 which are not locally finite.