Abstract
A C-1 map f : M -> M is called transversal if for all m is an element of N the graph of f(m) intersects transversally the diagonal of M x M at each point (x, x) being x a fixed point of f(m). Let CPn be the n-dimensional complex projective space, HPn be the n-dimensional quaternion projective space and S-p x S-q be the product space of the p-dimensional with the q-dimensional spheres, p not equal q. Then for the cases M equal to CPn, HPn and S-p x S-q we study the set of periods of f by using the Lefschetz numbers for periodic points.