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Vol. 48 No. 3 (2022)
Serdica Mathematical Journal

Articles

On the diagonal actions of Z on Z^n

https://doi.org/10.55630/serdica.2022.48.129-148

Published 15-10-2022

  • Jordan Sahattchieve

Abstract

In this paper, I study the actions of \(\mathbb{Z}\) on \(\mathbb{Z}^n\) from a dynamical perspective. The motivation for this study comes from the notion of bounded packing introduced by Hruska and Wise in 2009. I shall also introduce the notion of coset growth for a finitely generated group. My analysis yields the following two results: bounded packing in certain semidirect products of \(\mathbb{Z}^n\) with \(\mathbb{Z}\) and a bound of the coset growth of the copy of \(\mathbb{Z}\) on the right in \(\mathbb{Z}^2 \rtimes \mathbb{Z}\) for the non-nilpotent groups of this type.

2020 Mathematics Subject Classification:

20F65, 20F16, 20F19

Keywords

bounded packing, polycyclic groups, coset growth

Full text

Author Details

Jordan Sahattchieve

1113 Sofia, Bulgaria
e-mail: jantonov@umich.edu

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