  We show that the isomorphism problem is solvable in the class of central
extensions of word-hyperbolic groups, and that the isomorphism problem for
biautomatic groups reduces to that for biautomatic groups with finite centre.
We describe an algorithm that, given an arbitrary finite presentation of an
automatic group $\Gamma$, will construct explicit finite models for the skeleta
of $K(\Gamma,1)$ and hence compute the integral homology and cohomology of
$\Gamma$.
