Year: 2013
Type: preprint
Abstract: We show that finitely generated Abelian groups admit equal growth functions with respect to symmetric generating sets if and only if they have the same rank and the torsion parts have the same parity. In contrast, finitely generated Abelian groups admit equal growth functions with respect to monoid generating sets if and only if they have same rank. Moreover, we show that the size of the torsion part is in fact determined by the set of all growth functions of a finitely generated Abelian group.
Source: arXiv (Cornell University)
Authors: Loeh, Clara, Mann, Matthias
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2260669059