- #1
Bachelier
- 376
- 0
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?
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?