# Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Identity

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< Abstract Algebra | Group Theory | Group | Definition of a Group

Let G be a group with binary operation

## Usages[edit]

- The identity of G,
*e*_{G}, is in group G. - Group G has an identity
*e*_{G} - If
*g*is in G,*e*_{G}*g*=*g**e*_{G}=*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]

*e*_{G}always mean identity of group G throughout this section.- G has to be a group
- If
*a*is not in group G,*a**e*_{G}may not equal to*a* - If is not the binary operation of G,
*a**e*_{G}may not equal to*a*