Group

A group $G$ is a Set that satisfies the axioms of a group.

Axioms

1. Closure: $A,B\in G⟹AB\in G$
2. Associativity: $A,B,C\in G⟹(AB)C=A(BC)$
3. Identity: $\exists I\text{ s.t. }\forall A\in G,IA=AI=A$
4. Inverse: $\forall A\in S,A^{-1}\in S\text{ s.t. }A{A}^{-1}=A^{-1}A=I$