WTS, is that such set is a subgroup. I need to show closure under group operation and inverse. I can do the inverse which is usually the hardest part, but I'm stuck on the grp op. So let a in K and b in K, both have finite distinct conjugates. Their conjugates are in the group too. WTS is that ab in K too. if a, b in K then xax-1 = c in K and yay-1 consider xy(ab)(xy)-1 note since xax-1 and yay-1 are finite and distinct then x and y are finite and distinct hence xy and its inverse is finite hence xy(ab)(xy)-1 in K what do you think?