Work

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

Year: 2024

Type: article

Abstract: Our result contains as special cases the Frobenius theorem (1895) on the number of solutions to the equation x n = 1 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.

Source: Journal of Group Theory

DOI: 10.1515/jgth-2023-0111

Author: Elena K. Brusyanskaya

Institutions: Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Russian Science Foundation

Award: G7787288036