Embeddings into Finitely Presented Simple Groups

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Title (deu)

Speaker / Lecturer

Collin Bleak

U of St Andrews

Description (deu)

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.

Keywords (deu)

Asymptotic Group TheorySimple Groups

Subject (eng)

ÖFOS 2012 -- 101009 -- Geometry

Type (eng)

lecture

Language

[eng]

Persistent identifier

https://phaidra.univie.ac.at/o:1682875

Date created

2023-07-20