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

We determine the integral homology of PSL4(Z) in degrees up to 5 and determine its p-part in higher degrees for the primes p⩾5. Our method applies to other arithmetic groups; as illustrations we include descriptions of the integral homology of PGL3(Z[i]) and PGL3(Z[exp(2πi/3)]) in degrees up to 5.