Help with proof involving the set of 1-1 mappings of S onto itself.

arpitm08

I understand that ##f^{-1}##gf∈A(S), because g, f ∈ A(S).

We need to determine that it sets s1. How would we go about that though?

gopher_p

Well, we could maybe try to compute ##(f^{-1}gf)(s_1)##?

Remember, ##(f^{-1}gf)(s_1)=f^{-1}\left(g\left(f(s_1)\right)\right)##.

arpitm08

thanks for the answer cocksucker

gopher_p

okay ...

arpitm08

Sorry, my friend is an idiot sometimes. I really appreciate your help on everything. It helped a ton. Sorry about my friend again.