I'm new to Math Stack Exchange.
I saw a problem about a finite group, $G$, and a homomorphism that maps an element of $G$ onto another element of $G$ (the mapping doesn't necessarily have to be to a distinct element).
What exactly might this look like? Could someone give a super trivial example of what this would be?
Take $G = \{0\}$, the trivial group. Define $f \colon G \rightarrow G$ by $f(0) = 0$.
Take $G = {0,1}$ $0+0 = 0$, $1+0 = 0+1 = 1$, $1+1 = 0$. Take $f \colon G \rightarrow G$ by $f(0) = 0$, $f(1) = 1$.