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Can YOU Prove this SPECIAL Group is Abelian? | Group Theory CHALLENGE!
We prove the following beautiful theorem with a creative trick: If G is a group and if f is an isomorphism from G to itself such that: (1) f(x) ≠ x for all x ≠ e (the identity element of the group G) (2) f(f(x)) = x for all x in G (i.e., f is an "involution", or order 2 automorphism of the group G), then G is an abelian group. The video is ...
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