Solvable Subgroup Theorem for simplicial nonpositive curvature

Abstract

Given a group $G$ with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of $G$ is finitely generated and virtually abelian of rank at most $2$. In particular this gives a new proof of the above theorem for systolic groups. The main tools used in the proof are the Product Decomposition Theorem and the Flat Torus Theorem.