Let G be a group of order 15. Then the number ofone-one homomorphism on itselfis (Answer should be integer) ___________.Correct answer is '8'. Can you explain this answer?

Question

Answer

We know that everygroup oforder 15 is cyclic

⇒ G ≈ ℤ₁₅

Also we know thateveryone-one homomorphism from a finte group to itself is an automorphism.Also the number of automorphism form ℤ_m to ℤ_m is

⇒ The number of automorphism from ℤ₁₅ to ℤ₁₅ is

(15) = 8

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