1. The problem statement, all variables and given/known data Suppose that s1≠s2 are in S and f(s1)=s2, where f[itex]\in[/itex]A(S). Then if H = (f[itex]\in[/itex]A(S)|f(s1)=s1)) and K = (g[itex]\in[/itex]A(S)|g(s2)=s2) show that: a) If g[itex]\in[/itex]K, then f^-1 *g *f [itex]\in[/itex] H 2. Relevant equations I don't know. 3. The attempt at a solution I don't really know where to go with this problem. I don't understand what it means that g[itex]\in[/itex]K if in the definition of K involves g like that, shouldn't that be implied? Does it just mean that g(s2)=s2? Then how do I figure out the inverse of f? Since f(s1)=s2, would the inverse just be f^-1(s2)=s1? Then how would I got about multiplying inverse of f to g and f and proving they are in H?? Thanks in advance for any help.