WTS, is that such set is a subgroup.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# SUBSET K of elements in a group with finite distinct distinct conjugates

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