On the number of tuples of group elements satisfying a first-order formula
Group Theory
2024-10-17 v3
Abstract
Our result contains as special cases the Frobenius theorem (1895) on the~number of solutions to the equation 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.
Keywords
Cite
@article{arxiv.2306.16498,
title = {On the number of tuples of group elements satisfying a first-order formula},
author = {Elena K. Brusyanskaya},
journal= {arXiv preprint arXiv:2306.16498},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:1806.08870