Question 64
Let $n$ be a positive integer, and let $G$ be a finite group of order $n$. A function $f: G \to G$ is a *pseudoendomorphism* if $f(xyz) = f(x)f(y)f(z)$, for all $x, y, z$ in $G$.
a) If $n$ is odd, show that every pseudoendomorphism of $G$ is an endomorphism.
b) If $n$ is even, is every pseudoendomorphism of $G$ an endomorphism?
a) If $n$ is odd, show that every pseudoendomorphism of $G$ is an endomorphism.
b) If $n$ is even, is every pseudoendomorphism of $G$ an endomorphism?