Group $(G, *)$DefinitionLet $*$ be a binary operation on $G$.$$*:G\times G \to G$$ Binary operation $*: G\times G \to G$associative$a*(b*c)=(a*b)*c$ for $\forall\ a, b, c\in G$identity$\exists e\in G$ such that $\ a*e=e*a=a$ for $\forall\ a\in G$inverse$\exists a^{-1}\in G$ such that $\ a* a^{-1} = a^{-1}*a =e$ for $\forall\ a\in G$If $G$ sufficies the above conditons, it is called a group under..