Group is Homomorphic Image of Free Group

Theorem

Let $G$ be a group.

Then there exists:

a free group $F$

a homomorphism $\phi: G \to F$

such that $F$ is the image of $G$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): free group
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): free group