Equations in virtually abelian groups: languages and growth
Group Theory
2022-02-01 v4 Formal Languages and Automata Theory
Abstract
This paper explores the nature of the solution sets of systems of equations in virtually abelian groups. We view this question from two angles. From a formal language perspective, we prove that the set of solutions to a system of equations forms an EDT0L language, with respect to a natural normal form. Looking at growth, we show that the growth series of the language of solutions is rational. Furthermore, considering the set of solutions as a set of tuples of group elements, we show that it has rational relative growth series with respect to any finite generating set.
Keywords
Cite
@article{arxiv.2009.03968,
title = {Equations in virtually abelian groups: languages and growth},
author = {Alex Evetts and Alex Levine},
journal= {arXiv preprint arXiv:2009.03968},
year = {2022}
}
Comments
Final version, to appear in Internat. J. Algebra Comput