- #1
robertjordan
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Homework Statement
Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root.
Homework Equations
G being a group means it is a set with operation * satisfying:
1.) for all a,b,c in G, a*(b*c)=(a*b)*c
2.) there exists an e s.t. for all x in G, x*e=x
3.) for all x in G there exists an x' s.t. x'*x=e
The Attempt at a Solution
The only thing I have gotten so far is the reason why (-2)^2 and 2^2 both equaling 4 doesn't present a counterexample. The reason it doesn't is because (-2) has no square root so it is not in our group G.
... other than that I'm stuck..