Identity of Group is Unique/Proof 1

Theorem

Let $\struct {G, \circ}$ be a group which has an identity element $e \in G$.

Then $e$ is unique.

Proof

By the definition of a group, $\struct {G, \circ}$ is also a monoid.

The result follows by applying the result Identity of Monoid is Unique.

$\blacksquare$

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 33.1$. The definition of a group