Embedding free Burnside groups in finitely presented groups

2002/10/17 by S. V. Ivanov, Ivanov, S. V.
Mathematics · #20F05 #20F06 #20F38 #20F50 #FOS: Mathematics #Group Theory (math.GR) #Primary 20E06 #Secondary 43A07 #math.GR #msc:20E06 #msc:20F05 #msc:20F06 #msc:20F38 #msc:20F50 #msc:43A07

paper · pdf · doi:10.48550/arxiv.math/0210276

15 pages

arxiv created 2002/10/17 · arxiv updated 2009/11/30

Abstract

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.

Related

• Uniform non--amenability of free Burnside groups
• On subgroups of free Burnside groups of large odd exponent
• Subgroups of groups finitely presented in Burnside varieties
• The Burnside problem for odd exponents
• Amenable groups without finitely presented amenable covers