10. Fill in the details of the proof that the symmetric groups S and So are isomorphic if |4| = || as follows: let 0: A be a bijection. Define SS by p(0)=00000- for all o ESA P: So and prove the following: (a) p is well defined, that is, if o is a permutation of A then 0ooo0 is a permutation of N. (b) is a bijection from SA onto Sn. [Find a 2-sided inverse for p.] (c) p is a homomorphism, that is, 4(00T) = 4(o) o p(T). Note the similarity to the change of basis or similarity transformations for matrices (we shall see the connections between these later in the text).