- #1
PsychonautQQ
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- 10
Homework Statement
If G is a group of even order, show that it has an element g not equal to the identity such that g^2 = 1.
Homework Equations
None
The Attempt at a Solution
What I wrote:
If |G| = n, then g^n = 1 for some g in G. Thus, (g^(n/2))(g^(n/2)) = 1, so g^(n/2) is the element of order 2.
Is this a flawed argument? there guaranteed to be an element such that g^n = 1?