  Applying E. Kowalski's recent generalization of the large sieve we prove that
certain properties expected to be typical (irreducibility of the characteristic
polynomial, absence of squares among the matrix coefficients...) are indeed
verified by most (in a very explicit sense) of the elements of GL(n,A) with
fixed determinant (where A is an intermediate ring between Z and Q that we
specify) or by (special) orthogonal matrices with integral entries and fixed
spinor norm.
