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

Abstract
Let Γ(n;p) be the congruence subgroup of SL(n;Z) of level p. We study the homology and cohomology of Γ(n;p) as modules over SL(n;Fp) and apply our results to obtain an upper bound for the order of K3(Z).

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