Equations in virtually abelian groups: Languages and growth

Alex Evetts, Alex Levine*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
JournalInternational Journal of Algebra and Computation
Early online date16 Feb 2022
Publication statusE-pub ahead of print - 16 Feb 2022


  • EDT0L languages
  • Equations in groups
  • Growth of groups
  • Virtually abelian groups

ASJC Scopus subject areas

  • Mathematics(all)


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