rideabike
- 15
- 0
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\inS}.
Then \existsh\inS such that h\notinT. Since G is a group, h*h must equal e.
Does that work?