I was wondering if anyone knows a more efficient method of finding conjugacy classes than the one i am currently using.(adsbygoogle = window.adsbygoogle || []).push({});

tex/ Example D_6* =<x,y| x^3=1, y^4=1, yx=x^2y>

now to find the conjugacy classes of this group i would first write out

the orbit of x <x> ={ 1x1, xxx^2, x^2xx, yxy^3,....x^2y^2xy^2x^2,...etc}

then i would use the set relation yx=(x^2)y to work out each of these 12 conjugates individually. Once this is done i continue with <x^2>, <y> etc...

..the only short cut i have found is the theorem that says <x>intersection<y> = empty set or <x>=<y>. But even with this surely there is a quicker way??

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# Finding conjugacy classes

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