2023/08/18 by David J. Benson, Benson, David J., Jon Carlson +1
Mathematics · #20C20 #20J06 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2308.09579
openalex publication_date 2023/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group and k a field of characteristic p. It is conjectured in a paper of the first author and John Greenlees that the thick subcategory of the stable module category StMod(kG) consisting of modules whose cohomology is finitely generated over H^*(G,k) is generated by finite dimensional modules and modules with no cohomology. If the centraliser of every element of order p in G is p-nilpotent, this statement follows from previous work. Our purpose here is to prove this conjecture in two cases with non p-nilpotent centralisers. The groups involved are \mathbb Z/3r×Σ3 (r> 0) in characteristic three and \mathbb Z/2× A4 in characteristic two. As a consequence, in these cases the bounded derived category of C^*BG (cochains on BG with coefficients in k) is generated by C^*BS, where S is a Sylow p-subgroup of G.