On the Homology of Congruence Subgroups and K 3 (Z)

Abstract

Let Gamma(n;p) be the congruence subgroup of SL(n;Z) of level p. We study the homology and cohomology of Gamma(n;p) as modules over SL(n;F(p)) and apply our results to obtain an upper bound for the order of K(3)(Z).