Groups whose word problems are not semilinear

Abstract

Abstract Suppose that G is a finitely generated group and WP ⁡ ( G ) {\operatorname{WP}(G)} is the formal language of words defining the identity in G. We prove that if G is a virtually nilpotent group that is not virtually abelian, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then WP ⁡ ( G ) {\operatorname{WP}(G)} is not a multiple context-free language.