Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families

Daniel Groves; Michael Hull

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arXiv · 1704.03491

Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families

Daniel Groves·Michael Hull

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Abstract

We study the set of homomorphisms from a fixed finitely generated group into a family of groups which are `uniformly acylindrically hyperbolic'. Our main results reduce this study to sets of homomorphisms which do not diverge in an appropriate sense. As an application, we prove that any relatively hyperbolic group with equationally noetherian peripheral subgroups is itself equationally noetherian.

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Daniel Groves, Michael Hull. 2017-04-11. Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families. https://arxiv.org/abs/1704.03491

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