Group homomorphism/Definition

Group homomorphism

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

$\psi \colon G\longrightarrow H$

is called group homomorphism, if the equality

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

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