1. Solvable Subgroup Theorem for simplicial nonpositive curvature
- Author
-
Tomasz Prytuła
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Group Theory (math.GR) ,Curvature ,01 natural sciences ,Bounded function ,20F67 (Primary), 20F65, 20F69 (Secondary) ,0103 physical sciences ,FOS: Mathematics ,Torsion (algebra) ,010307 mathematical physics ,Finitely-generated abelian group ,0101 mathematics ,Abelian group ,Mathematics - Group Theory ,Mathematics - 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., 7 pages
- Published
- 2018
- Full Text
- View/download PDF