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FLOUR 09/07/21 6:51:39 PM #1: |
Let G be a group of finite order. I need to prove that the function f(x)=x^2 acts as an automorphism on G if and only if G is abelian with odd order.
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nothanks1 09/07/21 6:52:45 PM #2: |
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DespondentDeity 09/07/21 6:53:55 PM #4: |
We got a special report from Alex Jones here: math is gay, I think math is kinda gay
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trappedunderice 09/07/21 6:54:16 PM #5: |
Well you see
Since G G has odd order, that means G G is finite. So can be injective if and only if it is surjective. To formally prove surjectivity, argue by contradiction. Suppose there is a yG yG such that xG xG, (x)y (x)y. That implies there are two distinct x 1 ,x 2 x1,x2 such that (x 1 )=(x 2 ) (x1)=(x2) by injectivity. ... Copied to Clipboard!
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