Identity of a group is unique

Dependencies:

1. Group Used in definition

Identity of a group is unique.

Proof

Let $e_1$ and $e_2$ be identities of $G$.

• Since $e_1$ is identity, $e_1\ast e_2=e_2$.
• Since $e_2$ is identity, $e_1\ast e_2=e_1$.

Therefore, $e_1=e_2$.

Dependency for:

1. Conditions for a subset to be a subgroup

Info:

• Depth: 1
• Number of transitive dependencies: 1

Transitive dependencies:

1. Group