Let G be a group, h an element of G, and n a positive integer Let Zn G be defined by (i) h i for 0 i n Give a necessary and sufficient condition (in terms of h and n) for to be a homomorphism Prove your assertion ...

The map is a homomorphism if and only if h n e the identity i ...

Let G be a group, h an element of G, and n a positive integer. Let

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Let G be a group, h an element of G, and n a positive integer. Let ∅ : Zn → G be defined by ∅(i) = hⁱ for 0 ≤ i ≤ n. Give a necessary and sufficient condition (in terms of h and n) for ∅ to be a homomorphism. Prove your assertion.

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A First Course In Abstract Algebra

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Authors: John Fraleigh

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Find a necessary and sufficient condition on G such that the map described in the preceding exercise is a homomorphism for all choices of h, k G.
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Let G be a group, h an element of G, and n a positive integer. Let

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A First Course In Abstract Algebra

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