Primitivity of permutation groups, coherent algebras and matrices

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group. the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent algebras. (C) 2002 Elsevier Science (USA).