This is the proof of Cayley's Theorem in Rotman's book - Advanced Modern Algebra Part 2. 
I have a vague in the definition of $\tau_a$. Why did he said "if $a \ne 1$, then $\tau_a$ is not a homomorphism"?
2026-04-12 03:31:56.1775964716
A question on the proof of Cayley's Theorem
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Hint: What is $\tau_a(1)$, given the definition of $\tau_a$?