IMO 2017 Shortlist A3
Let S be a nite set, and let A be the set of all fun tions from S to S. Let f be an element of A, and let T “ fpSq be t...
Category: Algebra
Problem
Let S be a nite set, and let A be the set of all fun tions from S to S. Let f be an element of A, and let T “ fpSq be the image of S under f. Suppose that f ˝ g ˝ f ‰ g ˝ f ˝ g for every g in A with g ‰ f. Show that fpTq “ T. (India)