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Benzoate
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Homework Statement
Suppose that G is an Abelian group and H is a subgroup of G. If every element of H is a square and every element of G/H is a square , prove that every element of G is a square.
Homework Equations
The Attempt at a Solution
Let a and b be elements of G. The ab=ba since G is an abeleian group. If H is a subgroup of G, then doesn't H share the same opperations with G? If so, since every element of in H is a square, then a^2*b^2 =(aa)(bb)=(bb)(aa) since G is abelian, H should be abelian. Therefore , there is an element in G that is a square
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