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arXiv · 2306.16498

On the number of tuples of group elements satisfying a first-order formula

Elena K. Brusyanskaya
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Abstract

Our result contains as special cases the Frobenius theorem (1895) on the~number of solutions to the equation $x^n=1$ in a finite group and the Solomon theorem (1969) on the number of solutions in a group to systems of equations with fewer equations than unknowns. Instead of systems of equations, we consider arbitrary first-order formulae in the group language with constants. Our result substantially generalizes the Klyachko--Mkrtchyan theorem (2014) on this topic.

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Elena K. Brusyanskaya. 2023-06-28. On the number of tuples of group elements satisfying a first-order formula. https://arxiv.org/abs/2306.16498

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