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Relatively prime isomorphism groups
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dim&dimmer
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11
Sep22-09, 06:12 PM
P: 22
ok,
Z/mZ is a cyclic group (iso to Z mod(m)) with order m, and Z/nZ has order n.
Isomorphism preserves orders so ker(g) = mnZ iff m and n are coprime, so that the order of Z/mZ x Z/nZ is mn.
Does this complete the proof