Group homomorphism/Definition

Let ${\displaystyle {}(G,\circ ,e_{G})}$ and ${\displaystyle {}(H,\circ ,e_{H})}$ denote groups. A mapping

${\displaystyle \psi \colon G\longrightarrow H}$

is called group homomorphism, if the equality

${\displaystyle {}\psi (g\circ g')=\psi (g)\circ \psi (g')\,}$

holds for all ${\displaystyle {}g,g'\in G}$.