Equations in groups that are virtually direct products

TL;DR

This paper proves that solving equations with recognisable constraints is decidable in groups formed as virtually direct products of hyperbolic groups, extending the understanding of algebraic decision problems in complex group structures.

Contribution

It establishes the decidability of equations with recognisable constraints in a new class of groups, namely virtually direct products of hyperbolic groups.

Findings

Decidability of equations with recognisable constraints in these groups.

Extension of algebraic decision problem results to complex group structures.

Provides a framework for analyzing equations in virtually direct product groups.

Abstract

In this note, we show that the satisfiability of equations and inequations with recognisable constraints is decidable in groups that are virtually direct products of finitely many hyperbolic groups.