
STEWART PRIDDY, Department of Mathematics, Northwestern University, Evanston, Illinois 60208, USA 
Decomposing products of classifying spaces 
Let
be the product of two finite groups. The problem
of determining the stable type of the classifying space
, localized at a prime p, is often quite difficult due to the
complicated nature of the subgroups of G which generally do not
relate well to those of H and K. Of course, the usual stable
decomposition of a product of spaces
gives a decomposition of BG but these summands may be
decomposable, even in elementary cases such as
. In some situations however, the stable type of BG is closely
related to that of BH and BK. We say BG is smash
decomposable if the indecomposable summands of BG_{+} are given by
simply smashing together those of BH_{+} and BK_{+}, that is, a
complete splitting for BG_{+} localized at p has the form
(Joint work with John Martino and Jason Douma)