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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Originally Posted by r7iris 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 *. $\displaystyle c*a = c*c^{-1}a=a \mbox{ and }a*c=ac^{-1}c=a$ $\displaystyle a^{-1} = cac^{-1}$ The rest is trival.
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