A group is a non-empty set G together with a binary operation on ⁠ G ⁠, here denoted " ⁠ ⋅ ⋅ ⁠ ", that combines any two elements a and b of G to form an element of ⁠ G ⁠, denoted ⁠ a ⋅ ⋅ b ⁠, such that the following three requirements, known as group axioms, are satisfied: