Let a group G be generated by {ai |i ∈ I}, where I is some indexing set and ai ∈ G for all i ∈ I. Let ϕ : G → G' and μ: G → G' be two homomorphisms from G into a group G', such that ϕ(ai) = μ(ai) for every i ∈ I. Prove that ϕ = μ. [Thus, for example, a homomorphism of a cyclic group is completely determined by its value on a generator of the group.] [Hint: Use Theorem 7.6 and, of course, Definition 13.1.]
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.