Let $(S,\circ)$ be an [[Algebraic Structure|algebraic structure]]. Let $x,y\in S.$ - $xy$ is used instead of $x\circ y.$ - $e$ or $1$ is used for the [[Identity element of a binary operation|identity element]]. - $x^{-1}$ is used to denote the [[Inverse under a binary operation|inverse]] of $x$ under $\circ.$ - $x^{n}$ is used to denote the $n$th [[Integer Power of Group Element|power]] of $x.$