linguistic:translation, structural:summarization
Uniqueness of identity element

The group axioms imply that the identity element is unique; that is, there exists only one identity element: any two identity elements e {\displaystyle e} and f {\displaystyle f} of a group are equal, because the group axioms imply e = e ⋅ f = f {\displaystyle e=e\cdot f=f}. It is thus customary to speak of the identity element of the group.