Nilpotent groups with balanced presentations

2020/09/28 by Jonathan A. Hillman, Hillman, J. A.
Computer Science · Mathematics · #20F18 #20J05 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2009.13001

openalex publication_date 2020/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a torsion free nilpotent group G has a balanced presentations and Hirsch length h(G)>3 then β₁(G;ℚ)=2. There is just one such group which is torsion-free and of Hirsch length h=4, and none with h=5. We also construct a torsion-free nilpotent group G with h=6 and such that β₂(G;F)=β₁(G;F) for all fields F.

Citations

• On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups

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