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  1. #1
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    Group

    Let G be a group and let c be a fixed element of G. Define a new operation " * " on G by
    a*b=ac^(-1)b

    prove that the set G is a group under *.
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  2. #2
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    Quote Originally Posted by r7iris View Post
    Let G be a group and let c be a fixed element of G. Define a new operation " * " on G by
    a*b=ac^(-1)b

    prove that the set G is a group under *.
    c*a = c*c^{-1}a=a \mbox{ and }a*c=ac^{-1}c=a

    a^{-1} = cac^{-1}

    The rest is trival.
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