Acylindrical hyperbolicity and existential closedness

André, Simon

doi:10.1090/proc/15409

Acylindrical hyperbolicity and existential closedness
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by Simon André

Proc. Amer. Math. Soc. 150 (2022), 909-918

DOI: https://doi.org/10.1090/proc/15409

Published electronically: December 22, 2021

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Abstract:

Let $G$ be a finitely presented group, and let $H$ be a subgroup of $G$. We prove that if $H$ is acylindrically hyperbolic and existentially closed in $G$, then $G$ is acylindrically hyperbolic. As a corollary, any finitely presented group which is existentially equivalent to the mapping class group of a surface of finite type, to $\mathrm {Out}(F_n)$ or $\mathrm {Aut}(F_n)$ for $n\geq 2$ or to the Higman group, is acylindrically hyperbolic.

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