PreprintCC BY 4.0arXiv
Gluing diagrams part 1: A constructive solution for the Higman-Thompson group isomorphism problem
Abstract
This paper introduces gluing diagrams, a combinatorial tool to construct homomorphisms between the shift pseudogroups of directed graphs and thus also their full groups of shifts. We will establish which of these diagrams produce isomorphisms. As an application, using the interpretation of Higman-Thompson groups as full groups of shifts of specific graphs, we will describe a procedure that constructs gluing diagrams that explicitly describe the isomorphisms between Higman-Thompson groups, conjectured by Higman and whose existence was proven by Pardo arXiv:1006.1759. This procedure will follow Euclid's algorithm and will allow us to lift isomorphisms to higher arity.
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BibTeX
@misc{gorazd2026gluing,
title = {{Gluing diagrams part 1: A constructive solution for the Higman-Thompson group isomorphism problem}},
author = {Roman Gorazd},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.02889},
eprint = {2605.02889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02889},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gluing diagrams part 1: A constructive solution for the Higman-Thompson group isomorphism problem
AU - Roman Gorazd
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2605.02889
UR - https://arxiv.org/abs/2605.02889
AB - This paper introduces gluing diagrams, a combinatorial tool to construct homomorphisms between the shift pseudogroups of directed graphs and thus also their full groups of shifts. We will establish which of these diagrams produce isomorphisms. As an application, using the interpretation of Higman-Thompson groups as full groups of shifts of specific graphs, we will describe a procedure that constructs gluing diagrams that explicitly describe the isomorphisms between Higman-Thompson groups, conjectured by Higman and whose existence was proven by Pardo arXiv:1006.1759. This procedure will follow Euclid's algorithm and will allow us to lift isomorphisms to higher arity.
ER -