Stephen D. Smith and Kristin L. Umland

Stablilty of cohomology via double-coset products and suborbit diagrams

To appear in J. Algebra

Abstract

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 calcluations
in the recent literature on the cohomology of sporadic groups.