Explicit construction of benign subgroup for Higman's reversing operation

2025/06/14 by Mikaelian, V. H.
#20E06 #20E07 #20F05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2506.12442

Abstract

For the Higman reversing operation ρ and for a set of integer-valued functions \mathcal X the following has been proved. Let the subgroup A_{\mathcal X} be benign in the free group F, let the respective finitely presented overgroup K_{\mathcal X} with its finitely generated subgroup L_{\mathcal X} be given for A_{\mathcal X} explicitly, and let the set \mathcal Y = ρ\mathcal X be obtained from \mathcal X by the reversing operation ρ. Then A_{\mathcal Y} also is benign in F and, moreover, the finitely presented overgroup K_{\mathcal Y} with its finitely generated subgroup L_{\mathcal Y} can also be given explicitly for it. The current work is a step in development of a general algorithm for construction of explicit Higman embeddings of recursive groups into finitely presented groups.

Citations

• Auxiliary free constructions for explicit embeddings of recursive groups
• Progress around the Boone-Higman Conjecture
• The Higman operations and embeddings of recursive groups
• Embeddings using universal words in the free group of rank 2 (Russian version)
• A modified proof for Higman's embedding theorem
• Subvariety structures in certain product varieties of groups
• Subgroups of almost finitely presented groups
• The Conjugacy Problem and Higman Embeddings

Related

• Higman operations on integer sequences, and embeddings of recursive groups
• A modified proof for Higman's embedding theorem
• Malnormal Subgroups of Finitely Presented Groups
• Subgroups of groups finitely presented in Burnside varieties
• The Higman operations and embeddings of recursive groups