Embedding hyperbolic groups into finitely presented infinite simple groups

James Belk; Collin Bleak

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arXiv · 2306.14863

Embedding hyperbolic groups into finitely presented infinite simple groups

James Belk·Collin Bleak

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Abstract

The Boone--Higman conjecture is that every recursively presented group with solvable word problem embeds in a finitely presented simple group. We discuss a brief history of this conjecture and work towards it. Along the way we describe some classes of finitely presented simple groups, and we briefly outline work of Belk, Bleak, Matucci, and Zaremsky showing that the broad class of hyperbolic groups embeds in a class of finitely presented simple groups.

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James Belk, Collin Bleak. 2023-06-26. Embedding hyperbolic groups into finitely presented infinite simple groups. https://arxiv.org/abs/2306.14863

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