$\forall$$g$:Group\{i\}, $e$:$\mid$$g$$\mid$, $a$:$\mathbb{Z}$. {-}$a$ x($\ast$;e;$\sim$) $e$ = $\sim$($a$ x($\ast$;e;$\sim$) $e$) $\in$ $\mid$$g$$\mid$