THE COMBINATORICS AND THE HOMOLOGY OF THE POSET OF SUBGROUPS OF P-POWER INDEX

For a finite group G and a prime p the poset S(p) (G) of all subgroups H not-equal G of p-power index is studied. The Mobius number of the p oset is given and the homotopy type of the poset is determined as a we dge of spheres. We describe the representation of G on the homology gr oups of the order complex of S(p) (G) and show that this representatio n can be realized by matrices with entries in the set { + 1, - 1, 0}. Finally a CL-shellable subposet of S(p) (G) is exhibited for odd prime s p.