@article{BH74,
  author = {Boone, William W. and Higman, Graham},
  title = {An algebraic characterization of groups with soluble word problem},
  journal = {Journal of the Australian Mathematical Society},
  volume = {18},
  number = {1},
  year = {1974},
  pages = {41--53},
  doi = {10.1017/S1446788700019108}
}

@misc{BBMZsurvey,
  author = {Belk, James and Bleak, Collin and Matucci, Francesco and
            Zaremsky, Matthew C. B.},
  title = {Progress around the {Boone--Higman} conjecture},
  year = {2025},
  eprint = {2306.16356},
  archivePrefix = {arXiv},
  primaryClass = {math.GR},
  note = {Version 3, 22 May 2025},
  url = {https://arxiv.org/abs/2306.16356v3}
}

@misc{FoundationsCompanion,
  author = {{OpenAI}},
  title = {{Finite algebraic envelopes and the Boone--Higman conjecture}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Finite-algebraic-envelopes-and-the-Boone-Higman-conjecture-September-23-2026/paper.pdf}{OAI:Finite-algebraic-envelopes-and-the-Boone-Higman-conjecture-September-23-2026}},
  year = {2026}
}

@article{BelkZaremsky2022,
  author = {Belk, James and Zaremsky, Matthew C. B.},
  title = {Twisted {Brin--Thompson} groups},
  journal = {Geometry \& Topology},
  volume = {26},
  number = {3},
  year = {2022},
  pages = {1189--1223},
  doi = {10.2140/gt.2022.26.1189},
  url = {https://eprints.gla.ac.uk/280398/1/280398.pdf}
}

@article{KrsticMcCool1999,
  author = {Krsti{\'c}, Sava and McCool, James},
  title = {Presenting {$\mathrm{GL}_n(k\langle T\rangle)$}},
  journal = {Journal of Pure and Applied Algebra},
  volume = {141},
  number = {2},
  year = {1999},
  pages = {175--183},
  doi = {10.1016/S0022-4049(98)00022-X}
}

@article{Kleene38,
  author = {Kleene, S. C.},
  title = {On notation for ordinal numbers},
  journal = {The Journal of Symbolic Logic},
  volume = {3},
  number = {4},
  year = {1938},
  pages = {150--155},
  doi = {10.2307/2267778}
}

@article{Newman42,
  author = {Newman, M. H. A.},
  title = {On theories with a combinatorial definition of "equivalence"},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {43},
  number = {2},
  year = {1942},
  pages = {223--243},
  doi = {10.2307/1968867}
}

@article{BieriEckmann1974,
  author = {Bieri, Robert and Eckmann, Beno},
  title = {Finiteness properties of duality groups},
  journal = {Commentarii Mathematici Helvetici},
  volume = {49},
  year = {1974},
  pages = {74--83},
  doi = {10.1007/BF02566720}
}

@article{Brown1975,
  author = {Brown, Kenneth S.},
  title = {Homological criteria for finiteness},
  journal = {Commentarii Mathematici Helvetici},
  volume = {50},
  year = {1975},
  pages = {129--135},
  doi = {10.1007/BF02565740}
}

@article{EilenbergZilber1953,
  author = {Eilenberg, Samuel and Zilber, J. A.},
  title = {On products of complexes},
  journal = {American Journal of Mathematics},
  volume = {75},
  number = {1},
  year = {1953},
  pages = {200--204},
  doi = {10.2307/2372629}
}

@book{Hatcher2002,
  author = {Hatcher, Allen},
  title = {Algebraic Topology},
  publisher = {Cambridge University Press},
  year = {2002},
  note = {Author's corrected electronic version},
  url = {https://pi.math.cornell.edu/~hatcher/AT/ATpage.html}
}

@incollection{Tho80,
  author = {Thompson, Richard J.},
  title = {Embeddings into finitely generated simple groups which preserve the word problem},
  booktitle = {Word Problems II},
  editor = {Adian, S. I. and Boone, W. W. and Higman, G.},
  series = {Studies in Logic and the Foundations of Mathematics},
  volume = {95}, publisher = {North-Holland}, year = {1980}, pages = {401--441},
  doi = {10.1016/S0049-237X(08)71348-X}
}

@article{BBMZhyperbolic,
  author = {Belk, James and Bleak, Collin and Matucci, Francesco and Zaremsky, Matthew C. B.},
  title = {Hyperbolic groups satisfy the {Boone--Higman} conjecture},
  journal = {Duke Mathematical Journal},
  volume = {175}, number = {9}, year = {2026}, pages = {1519--1592},
  doi = {10.1215/00127094-2025-0055},
  url = {https://arxiv.org/abs/2309.06224v3}
}

@misc{BFFHZ,
  author = {Belk, James and Fournier-Facio, Francesco and Hyde, James and Zaremsky, Matthew C. B.},
  title = {{Boone--Higman} embeddings of {$\mathrm{Aut}(F_n)$} and mapping class groups of punctured surfaces},
  year = {2026}, eprint = {2503.21882}, archivePrefix = {arXiv}, primaryClass = {math.GR},
  note = {Version 3, 17 September 2026. To appear in Proceedings of the London Mathematical Society},
  url = {https://arxiv.org/abs/2503.21882v3}
}

@article{Higman1961,
  author = {Higman, Graham},
  title = {Subgroups of finitely presented groups},
  journal = {Proceedings of the Royal Society of London. Series A},
  volume = {262}, number = {1311}, year = {1961}, pages = {455--475},
  doi = {10.1098/rspa.1961.0132}
}

@article{Brown1987,
  author = {Brown, Kenneth S.},
  title = {Finiteness properties of groups},
  journal = {Journal of Pure and Applied Algebra},
  volume = {44}, number = {1--3}, year = {1987}, pages = {45--75},
  doi = {10.1016/0022-4049(87)90015-6}
}

@misc{BHMgerms,
  author = {Belk, James and Hyde, James and Matucci, Francesco},
  title = {Finite germ extensions},
  year = {2024}, eprint = {2407.03149}, archivePrefix = {arXiv},
  primaryClass = {math.GR}, note = {Version 1, 3 July 2024},
  url = {https://arxiv.org/abs/2407.03149v1}
}

@misc{FFKLZstabilizers,
  author = {Fournier-Facio, Francesco and Kropholler, Peter H. and
            Lyman, Robert Alonzo and Zaremsky, Matthew C. B.},
  title = {Finiteness properties of stabilisers of oligomorphic actions},
  year = {2026}, eprint = {2506.02319}, archivePrefix = {arXiv},
  primaryClass = {math.GR}, note = {Version 2, 27 February 2026},
  url = {https://arxiv.org/abs/2506.02319v2}
}

@article{BDH1980,
  author = {Baumslag, Gilbert and Dyer, Eldon and Heller, Alex},
  title = {The topology of discrete groups},
  journal = {Journal of Pure and Applied Algebra},
  volume = {16}, year = {1980}, pages = {1--47},
  doi = {10.1016/0022-4049(80)90040-7}
}