Progress around the Boone-Higman conjecture

James Belk; Collin Bleak; Francesco Matucci; Matthew C. B. Zaremsky

Progress around the Boone-Higman conjecture

James Belk
, Collin Bleak
, Francesco Matucci
, Matthew C. B. Zaremsky

Research output: Working paper › Preprint

Abstract

A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group G has solvable word problem if and only if G 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.

Original language	English
Publisher	arXiv
Number of pages	21
Publication status	Published - 28 Jun 2023

Keywords

Group theory

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https://arxiv.org/abs/2306.16356Licence: Other

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1 Article

Progress around the Boone-Higman conjecture
Belk, J., Bleak, C., Matucci, F. & Zaremsky, M. C. B., 16 Jun 2025, (E-pub ahead of print) In: EMS Surveys in Mathematical Sciences. Online First, 28 p.
Research output: Contribution to journal › Article › peer-review

Open Access

Cite this

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title = "Progress around the Boone-Higman conjecture",

abstract = "A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group G has solvable word problem if and only if G 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 = "Group theory",

author = "James Belk and Collin Bleak and Francesco Matucci and Zaremsky, \{Matthew C. B.\}",

note = "Funding: FM is a member of the Gruppo Nazionale per le Strutture Algebriche, Geomet- riche e le loro Applicazioni (GNSAGA) of the Istituto Nazionale di Alta Matem- atica (INdAM) and gratefully acknowledges the support of the Funda¸c˜ao para a Ciˆencia e a Tecnologia (CEMAT-Ciˆencias FCT projects UIDB/04621/2020 and UIDP/04621/2020) and of the Universit`a degli Studi di Milano–Bicocca (FA project 2020-ATE-0006 “Strutture Algebriche”). MCBZ is supported by grant \#635763 from the Simons Foundation.",

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AU - Matucci, Francesco

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N1 - Funding: FM is a member of the Gruppo Nazionale per le Strutture Algebriche, Geomet- riche e le loro Applicazioni (GNSAGA) of the Istituto Nazionale di Alta Matem- atica (INdAM) and gratefully acknowledges the support of the Funda¸c˜ao para a Ciˆencia e a Tecnologia (CEMAT-Ciˆencias FCT projects UIDB/04621/2020 and UIDP/04621/2020) and of the Universit`a degli Studi di Milano–Bicocca (FA project 2020-ATE-0006 “Strutture Algebriche”). MCBZ is supported by grant #635763 from the Simons Foundation.

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N2 - A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group G has solvable word problem if and only if G 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.

AB - A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group G has solvable word problem if and only if G 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.

KW - Group theory

M3 - Preprint

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PB - arXiv

ER -

Progress around the Boone-Higman conjecture

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Research output

Progress around the Boone-Higman conjecture

Cite this