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Math Help - ABSTRACT ALGEBRA _GROUPs

  1. #1
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    ABSTRACT ALGEBRA _GROUPs

    Can someone please help me with this quesion?
    If G an abelian Group Prove that (a*b)^n = a^n * b^n

    Thanks
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  2. #2
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    Quote Originally Posted by Godisgood View Post
    Can someone please help me with this quesion?
    If G an abelian Group Prove that (a*b)^n = a^n * b^n

    Thanks
    rewrite (a*b)^n= a*b*a*b*a*b*a*b*.....*a*b with n pairs. Since G is abelian we can commute the elements. bring all the a's to the left and the b's to the right and get

    a*a*a*a*...*a*b*b*b*....*b, n times each. This equals a^n * b^n.

    Note that it is very important that G is abelian. If not, we cannot rearrange the terms however we like!
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