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Math Help - showthat...

  1. #1
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    Unhappy showthat...

    a) in every group G, for all a,b members of G, and for all n member of Z(integers): (a^-1 * b * a)^n= a^-1 * b^n * a

    (Do you have to use induction for this, because i think you do, but i am unsure?)

    b) Every group table for a finite group is a Latian square, that is, each element of the group appears exactly once in each row and each column.
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    a) in every group G, for all a,b members of G, and for all n member of Z(integers): (a^-1 * b * a)^n= a^-1 * b^n * a
    Just look at what happens: (a^{-1} ba)^n = (a^{-1} ba)(a^{-1} ba)(a^{-1} ba) .... = a^{-1} b(aa^{-1})b(aa^{-1}) ... a= a^{-1} b^n a

    b) Every group table for a finite group is a Latian square, that is, each element of the group appears exactly once in each row and each column.
    Hint: The equation ax=b always a solution in a group.
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