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Let p be a prime. (a) Prove that Z/pZ ⊕ Z/pZ has exactly p + 1...

  • Let p be a prime.

    (a) Prove that Z/pZ ⊕ Z/pZ has exactly p + 1 subgroups of order p.
    (b) How many subgroups of order p does Z/pZ ⊕ Z/pZ ⊕ Z/pZ have? Can you generalize further? Explain.

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