Subgroups of groups finitely presented in Burnside varieties
Alexander Olshanskii

TL;DR
The paper proves a version of Higman's embedding theorem for groups in Burnside varieties with large odd exponents, showing that certain finitely generated groups can be embedded into finitely presented groups within the same variety.
Contribution
It establishes a Higman-type embedding theorem for Burnside varieties with large odd exponents, demonstrating the existence of a universal finitely presented group in this setting.
Findings
Finitely generated groups in ${ m Burnside}_n$ embed into finitely presented groups in the same variety.
Existence of a universal 2-generated finitely presented group in ${ m Burnside}_n$ containing all finitely presented groups as subgroups.
Extension of Higman's embedding theorem to Burnside varieties with large odd exponents.
Abstract
For all sufficiently large odd integers , the following version of Higman's embedding theorem is proved in the variety of all groups satisfying the identity . A finitely generated group from has a presentation with a finite set of generators and a recursively enumerable set of defining relations if and only if it is a subgroup of a group finitely presented in the variety . It follows that there is a 'universal' -generated finitely presented in group containing isomorphic copies of all finitely presented in groups as subgroups.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · graph theory and CDMA systems
