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Math Help - Show a quotient group is abelian

  1. #1
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    Show a quotient group is abelian

    Let A be an abelian group and let B be a subgroup of A. Prove that A/B is abelian.
    So this is what I have:

    Let x, y \in A, then xB, yB \in A/B. We must show xB \cdot yB = yB \cdot xB
    Since B is a subgroup of A and A is abelian, then B is a normal subgroup of B.
    We compute:
    xB \cdot yB  = (xy)B because B is a normal subgroup of A.
    = (yx)B because A is abelian
    = yB \cdot xB

    And so A/B is abelian. Is this right?
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  2. #2
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    Re: Show a quotient group is abelian

    Yes, that is correct.
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