Progress around the Boone-Higman Conjecture
Group Theory
2025-05-23 v3
Abstract
A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group has solvable word problem if and only if can be embedded into a finitely presented simple group. We comment on the history of this conjecture and survey recent results that establish the conjecture for many large classes of interesting groups.
Cite
@article{arxiv.2306.16356,
title = {Progress around the Boone-Higman Conjecture},
author = {James Belk and Collin Bleak and Francesco Matucci and Matthew C. B. Zaremsky},
journal= {arXiv preprint arXiv:2306.16356},
year = {2025}
}
Comments
v2: minor changes, submitted version. v3: accepted version, to appear in EMS Surv. Math. Sci