Sur l'application de Quillen pour la cohomologie modulo 2 de certains groupes finis

2025/01/07 by Jean Lannes, Lannes, Jean
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2501.03953

openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group. In a famous article, Quillen describes an F-isomorphism between commutative ℕ-graded \mathbbF₂-algebras q_G:H^*(G;\mathbbF₂)\toL(G) , with L(G) defined in terms of the elementary abelian 2-groups contained in G. We show that q_G is in fact an actual isomorphism for three families of finite groups: symmetric groups, alternating groups and finite Coxeter groups.

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