Equations in virtually abelian groups: Languages and growth

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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
Pages (from-to)411-442
JournalInternational Journal of Algebra and Computation
Issue number03
Publication statusPublished - 16 Feb 2022


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


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