# Math Help - Group

1. ## 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 *.

2. 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 *.
$c*a = c*c^{-1}a=a \mbox{ and }a*c=ac^{-1}c=a$

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

The rest is trival.