Cohomological finiteness properties of the Brin-Thompson-Higman groups 2V and 3V

2010/09/23 by Dessislava H. Kochloukova, Kochloukova, Dessislava H., Conchita Martı́nez-Pérez +4
Mathematics · #20J05 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20J05

paper · pdf · doi:10.48550/arxiv.1009.4600

26 pages, 18 figures, revised version

openalex publication_date 2010/09/23 · arxiv created 2010/12/10 · arxiv updated 2010/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Brin's generalisations 2V and 3V of the Thompson-Higman group V are of type FP_∞. Our methods also give a new proof that both groups are finitely presented.

Related

• Cohomological finiteness conditions and centralisers in generalisations of Thompson's group V
• Bredon cohomological finiteness conditions for generalisations of\n Thompson's groups
• Finiteness properties for relatives of braided Higman--Thompson groups
• Finite presentability of twisted Brin-Thompson groups
• Generalisations of Thompson's group V arising from purely infinite groupoids