Elementary divisors of tensor products and p-ranks of binomial matrices

Let be a field of characteristic p and let A and B be two Jordan blocks with nonzero eigenvalues. The reduction formulas of C.W. Norman enable us to compute the elementary divisors of A B. We investigate connections between the elementary divisors of A B and binomial matrices. In particular, we show that Norman’s reduction formulas can be used to compute the p-rank of certain binomial matrices.