Subgroups of groups finitely presented in Burnside varieties

2019/09/23 by Alexander Olshanskii, Olshanskii, Alexander
Computer Science · Engineering · Mathematics · #03D10 #03D25 #20E06 #20E10 #20F05 #20F06 #20F10 #20F50 #20F65 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1909.10113

openalex publication_date 2019/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For all sufficiently large odd integers n, the following version of Higman's embedding theorem is proved in the variety \cal B_n of all groups satisfying the identity xⁿ=1. A finitely generated group G from \cal B_n has a presentation G=⟨ A| R⟩ with a finite set of generators A and a recursively enumerable set R of defining relations if and only if it is a subgroup of a group H finitely presented in the variety \cal B_n. It follows that there is a 'universal' 2-generated finitely presented in \cal B_n group containing isomorphic copies of all finitely presented in \cal B_n groups as subgroups.

Related

• Embedding free Burnside groups in finitely presented groups
• Malnormal Subgroups of Finitely Presented Groups
• A modified proof for Higman's embedding theorem
• The Conjugacy Problem and Higman Embeddings
• An explicit algorithm for the Higman Embedding Theorem