Embeddings into Finitely Presented Simple Groups

Collin Bleak (U of St Andrews)

Jul 20. 2023, 09:00 — 09:45

In this talk, we describe a process whereby we can embed any hyperbolic group into a finitely presented infinite simple group.  This gives a proof of what is, in some sense, the ​``typical'' case of the Boone-Higman Conjecture of 1973 (that a finitely generated grouip G has a solvable word problem if and only if G can be embedded into a finitely generated simple group).

  The talk will proceed in three roughly independent parts: A short history of the Boone-Higman conjecture, a discussion of hyperbolic groups and an embedding of these into the Rational group of Grigorchuk, Nekrashevych, and Suschanskii, and finally, a discussion of why the topological full group over this rational group is finitely presented and simple, or, at least provides a route to a further embedding into a group that is finitely presented and simple.

Joint with James Belk, Francesco Matucci, and Matthew Zaremsky.

Further Information
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics (Workshop)
Christopher Cashen (U of Vienna)
Javier de la Nuez González (KIAS, Seoul)
Alexandra Edletzberger (U of Vienna)
Yash Lodha (U of Hawaii, Honolulu)