First Author: Rafael Villarroel-Flores Address: Instituto de Matematicas, UNAM, Circuito Exterior, Ciudad Universitaria, Mexico, D.F., Mexico Second Author: Peter Wehh Address: School of Mathematics, University of Minnesota, Minneapolis MN 55455 USA Title: Some split exact sequences in the cohomology of groups Abstract: We analyze the split exact sequences of (co)homology groups associated to the spaces of Dwyer which give rise to the centralizer decomposition and subgroup decomposition of the classifying space BG of a finite group. In the first instance these sequences have infinite length. We show that they give rise to finite sequences which are also split and exact. The sequences arise as the first page of a spectral sequence. Preprint: January, 2000.