Propagating sharp group homology decompositions
arXiv:math/0402270 · doi:10.1016/j.aim.2005.01.006
Abstract
A collection C of subgroups of a finite group G can give rise to three different standard formulas for the cohomology of G in terms of either: the subgroups in C; or their centralizers; or their normalizers. We give a short but systematic study of the relationship among such formulas for nine standard collections C of p-subgroups, obtaining some new formulas in the process. To do this, we exhibit some sufficient conditions on the poset C which imply comparison results.
12 pages. Extra counterexamples added. To appear in Advances in Math