English

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 GG has solvable word problem if and only if GG 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.

Keywords

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

R2 v1 2026-06-28T11:17:05.214Z