Let a group G be generated by { a i | i I}, where I is
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Let a group G be generated by { ai | i ∈ I}, where I is some indexing set and ai ∈ G for all i ∈ I. Let ∅ : G → G' and µ : G → G' be two homomorphisms from G into a group G', such that ∅(ai) = µ(ai) for every i ∈ I. Prove that ∅ = µ. [Thus, for example, a homomorphism of a cyclic group is completely determined by its value on a generator of the group.]
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Since and are homomorphisms they preserve the group operation in G This m...View the full answer
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