Even Order Group has Order 2 Element/Proof 2
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Theorem
Let $G$ be a group whose identity is $e$.
Let $G$ be of even order.
Then:
- $\exists x \in G: \order x = 2$
That is:
- $\exists x \in G: x \ne e: x^2 = e$
Proof
This is a direct corollary of the stronger result Even Order Group has Odd Number of Order 2 Elements.
$\blacksquare$