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rideabike
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Homework Statement
Let (G,*) be a finite group of even order. Prove that there exists some g in G such that g≠e and g*g=e. [where e is the identity for (G,*)]
Homework Equations
Group properties
The Attempt at a Solution
Let S = G - {e}. Then S is of odd order, and let T={g,g^-1: g[itex]\in[/itex]S}.
Then [itex]\exists[/itex]h[itex]\in[/itex]S such that h[itex]\notin[/itex]T. Since G is a group, h*h must equal e.
Does that work?