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Answering a question of Geoff Robinson, we compute the large n limitingproportion of i(n,q)/q^[n^2/2], where i(n,q) denotes the number of involutionsin GL(n,q). We give similar results for the finite unitary, symplectic, andorthogonal groups, in both odd and even characteristic. At the heart of thiswork are certain new "sum=product" identities. Our self-contained treatment ofthe enumeration of involutions in even characteristic symplectic and orthogonalgroups may also be of interest.

Asymptotics of the number of involutions in finite classical groups