Year: 2016
Type: preprint
Abstract: We study the HNN extension of $\mathbb{Z}^m$ given by the cubing endomorphism $g\mapsto g^3$, and prove that such groups have rational growth. To do so, we describe a method of computing the subgroup growth series of the horocyclic subgroup $\mathbb{Z}^m$ in this family of examples, prove that for all $m$ the group has rational growth. In the appendix, the subgroup growth series has been computed for all $m \leq 10$.
Source: arXiv (Cornell University)
Authors: Sánchez, Ayla P., Shapiro, Michael
Institutions: Wheaton College - Illinois, University of Bath
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950364896