Solvable Subgroup Theorem for simplicial nonpositive curvature

TL;DR

This paper proves that solvable subgroups of groups acting properly on systolic complexes are finitely generated and virtually abelian of rank at most 2, using geometric group theory tools.

Contribution

It establishes a solvable subgroup theorem for systolic groups, providing a new proof and extending understanding of subgroup structure in nonpositive curvature contexts.

Findings

Solvable subgroups are finitely generated and virtually abelian of rank ≤ 2

Provides a new proof of the subgroup theorem for systolic groups

Utilizes Product Decomposition and Flat Torus Theorems

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.