On the girth of groups acting on CAT(0) cube complexes
Abstract
We obtain a sufficient condition for lattices in the automorphism group of a finite-dimensional CAT(0) cube complex to have infinite girth.As a corollary, we get a version of the girth alternative for groups acting geometrically on CAT(0) cube complexes: any such group is either {locally finite}-by-{virtually abelian} or it has infinite girth.We produce counterexamples to show that the alternative fails in the general class of groups acting cocompactly on finite-dimensional CAT(0) cube complexes using examples of nonvirtually solvable groups which satisfy a law.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 7
- Pages
- 2539–2558
- Publication date
- 1 September 2026
- Language
- EN