(1) | \begin{equation} \forall \, x, y \in X : x y \in X \end{equation} |
(2) | \begin{equation} \forall \, x, y, z \in X : (x y) z = x (y z) \end{equation} |
(3) | \begin{equation} \exists \, 1_G \in X : \forall \, x \in X : 1_G x = x 1_G = x \end{equation} |
(4) | \begin{equation} \forall \, x \in X : \exists \, x^{-1} \in X : x^{-1} x = x x^{-1} = 1_G \end{equation} |