Equation Problem over central extensions of hyperbolic groups

TL;DR

This paper proves that the Equation Problem, which determines the solvability of systems of equations, is solvable in central extensions of hyperbolic groups, expanding understanding of algorithmic problems in group theory.

Contribution

It demonstrates the solvability of the Equation Problem specifically within central extensions of hyperbolic groups, a previously unresolved case.

Findings

Equation Problem is solvable in central extensions of hyperbolic groups

Provides an algorithmic solution for a class of group-theoretic problems

Advances understanding of decision problems in geometric group theory

Abstract

The Equation Problem in finitely presented groups asks if there exists an algorithm which determines in finite amount of time whether any given equation system has a solution or not. We show that the Equation Problem in central extensions of hyperbolic groups is solvable.