Elementary amenable groups of cohomological dimension 3

2021/02/05 by Jonathan A. Hillman, Hillman, Jonathan A.
Mathematics · #20F16 #20J06 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2102.02947

openalex publication_date 2021/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that torsion-free elementary amenable groups of Hirsch length ≤3 are solvable, of derived length ≤3. This class includes all solvable groups of cohomological dimension 3. We show also that groups in the latter subclass are either polycyclic, semidirect products BS(1,n)\rtimesℤ or properly ascending HNN extensions with base ℤ² or π₁(Kb).

Related

• Dimension of elementary amenable groups
• Finite dimensional amenable groups
• Non-solvable torsion-free virtually solvable groups
• Homological Dimension of Solvable Groups
• Amenable groups of finite cohomological dimension and the zero divisor conjecture