On Equational Noetherianity of Colorable Hierarchically Hyperbolic Groups

TL;DR

This paper proves that homomorphisms from any finitely generated group to strictly acylindrical colorable hierarchically hyperbolic groups satisfy the ascending chain condition on algebraic sets, establishing their equational noetherianity.

Contribution

It establishes the equational noetherianity of strictly acylindrical colorable hierarchically hyperbolic groups, a significant class in geometric group theory.

Findings

Any homomorphism from a finitely generated group to these groups is controlled by finitely many equations.

The class of strictly acylindrical colorable hierarchically hyperbolic groups is equationally noetherian.

The result extends understanding of algebraic properties of complex hyperbolic groups.

Abstract

We study the homomorphisms from a fixed finitely generated group to strictly acylindrical colorable hierarchically hyperbolic groups. We prove that any such group is equationally noetherian.