Topology and Geometric Group Theory Seminar
A group is equationally noetherian if it satisfies a group-theoretic version of the Hilbert Basis
Theorem. This property is important for understanding solutions to systems of equations in a
group G, or equivalently understanding sets of homomorphisms to G. Furthermore, this property
naturally generalizes to families of groups. We will discuss some basic properties of equationally
noetherian groups and families and we will give a criteria for an acylindrically hyperbolic group
(or family of groups) to be equationally noetherian. As an application, we show that groups which
are hyperbolic relative to equationally noetherian subgroups are equationally noetherian.