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.

It is shown that the SL(2, C)-Poincare associative algebraic model of B6hm can be extended without essential difficulty to an SL(2, C)-de Sitter model which gives rise to a meson mass formula with both spin and isospin dependence.

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