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We determine the integral homology of PSL4(Z) in degrees at most 5 anddetermine its p-part in higher degrees for the primes p>=5. Our method appliesto other arithmetic groups; as illustrations we include descriptions of theintegral homology of PGL3(Z[i]) and PGL3(Z[\exp(2\pi{i}/3)]) in degrees at most5.

On the integral homology of PSL4(Z) and other arithmetic groups