Can anybody please help me with this question???
Let $G$ and $G'$ be groups with $G$ simple.
Prove that if $|G| > |G'|$, then the only homomorphism $\varphi : G → G'$ is the trivial one.
2026-03-27 16:46:29.1774629989
Homomorphism defined on a simple group
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Hint: The kernel of any homomorphism $f: G \to G'$ is a normal subgroup of $G$.