(7) Determine all subgroups of Z. For each subgroup H

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(7) Determine all subgroups of Z. For each subgroup H <Z,
(a) Find a group homomorphism µ : Z → Z such that ☀(Z) = H.
(b) Find an integer n and a group homomorphism H: Z → Zn so that
'H
H = {a € Z | H(a) = 0}.
Transcribed Image Text:(7) Determine all subgroups of Z. For each subgroup H <Z, (a) Find a group homomorphism µ : Z → Z such that ☀(Z) = H. (b) Find an integer n and a group homomorphism H: Z → Zn so that 'H H = {a € Z | H(a) = 0}.
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