Application Of the Pushout Formula of Generalized Lefschetz Number

A self-mapping having preferably characteristic on topological space is obtained and is homotopic to power-equate self-mapping based on the inducing action on the fundamental group of the space and the point homotopy.By using the characteristic and pushout formula of generalized Lefschetz number,we prove that the Nielsen number of power-equate self-mapping is not more than unit.