Corpus ID: 119122657

Growth rate of endomorphisms of Houghton's groups

  title={Growth rate of endomorphisms of Houghton's groups},
  author={Jong Bum Lee and Sang R Lee},
  journal={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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