Geodesic
On the diagonal actions of Z on Z^n
Serdica Mathematical Journal, Tome 48 (2022) no. 3, pp. 129-148.

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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.
Keywords: bounded packing, polycyclic groups, coset growth, 20F65, 20F16, 20F19 
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Sahattchieve, Jordan. On the diagonal actions of Z on Z^n. Serdica Mathematical Journal, Tome 48 (2022) no. 3, pp. 129-148. http://geodesic.mathdoc.fr/item/SMJ2_2022_48_3_a0/