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4. Let f : G→H be a group homomorphism. Suppose a∈G is an element of finite...

4. Let f : G→H be a group homomorphism. Suppose a∈G is an element of finite order n.

(a) Prove that f(a) has finite order k, where k is a divisor of n.

(b) If f is an isomorphism, prove that k=n.

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