Corpus ID: 119122657

# Growth rate of endomorphisms of Houghton's groups

@article{Lee2015GrowthRO,
title={Growth rate of endomorphisms of Houghton's groups},
author={Jong Bum Lee and Sang R Lee},
journal={arXiv: Group Theory},
year={2015}
}
• Published 30 November 2015
• Mathematics
• arXiv: Group Theory
A Houghton's group $\mathcal{H}_n$ consists of translations at infinity of a $n$ rays of discrete points on the plane. In this paper we study the growth rate of endomorphisms of Houghton's groups. We show that if the kernel of an endomorphism $\phi$ is not trivial then the growth rate $\mathrm{GR}(\phi)$ equals either $1$ or the spectral radius of the induced map on the abelianization. It turns out that every monomorphism $\phi$ of $\mathcal{H}_n$ determines a unique natural number $\ell$ such… Expand

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