Centric linking systems of locally finite groups

2017/02/13 by Rémi Molinier, Molinier, Rémi
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.1702.03995

openalex publication_date 2017/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These notes are defining the notion of centric linking system for a locally finite group If a locally finite group G has countable Sylow p-subgroups, we prove that, with a countable condition on the set of intersections, the p-completion of its classifying space is homotopy equivalent to the p-completion of the nerve of its centric linking system.

Related

• Subgroup collections controlling the homotopy type of a p-local compact group
• Fusion systems and localities
• Commuting partial normal subgroups and regular localities
• Local Sylow theory of totally disconnected, locally compact groups
• Rigid automorphisms of linking systems of finite groups of Lie type