Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Identity
Let G be a group with binary operation
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Algebra_Proof_Diagram_Identity.svg/180px-Algebra_Proof_Diagram_Identity.svg.png)
1. Group G has an identity eG.
2. eG*c = c*eG = c if c is in Group G
Usages
edit- The identity of G, eG, is in group G.
- Group G has an identity eG
- If g is in G, eG g = g eG = g
- e is the identity of group G if
- e is in group G, and
- e g = g e = g for every element g in G.
Notice
edit- eG always mean identity of group G throughout this section.
- G has to be a group
- If a is not in group G, a eG may not equal to a
- If is not the binary operation of G, a eG may not equal to a