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.
Original language | English |
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Pages (from-to) | 411-442 |
Number of pages | 32 |
Journal | International Journal of Algebra and Computation |
Volume | 32 |
Issue number | 3 |
Early online date | 16 Feb 2022 |
DOIs | |
Publication status | Published - May 2022 |
Keywords
- EDT0L languages
- Equations in groups
- Growth of groups
- Virtually abelian groups
ASJC Scopus subject areas
- General Mathematics