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On endomorphisms of automatic groups

Preprint

We propose two geometric versions of the bounded reduction property and find conditions for them to coincide. In particular, for the natural automatic structure on a hyperbolic group, the two notions are equivalent. We study endomorphisms with $L$-quasiconvex image and prove that those with finite kernel satisfy a synchronous version of the bounded reduction property. Finally, we use these techniques to prove $L$-quasiconvexity of the equalizer of two endomorphisms under certain (strict) conditions.

Publication

Year of publication: 2021

Identifiers

Other: arXiv:2110.08309v1

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Preprint

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