Stability of Cohomology via Double-Coset Products and Suborbit Diagrams Original Research Article

Stability of subgroup cohomology is typically defined by a condition on individual double cosets, though use of the natural multiplication among them can reduce the amount of direct checking needed. The study of geometries for many finite groups, notably the sporadic simple groups, has frequently included the determination of suborbit diagrams, from which the needed multiplication coefficients are immediately available. The technique is applied to simplify certain calculations in the recent literature on the cohomology of the sporadic groups.