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Group Theory Proof Form

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Let G be a finite group with K is a normal subgroup of G. If (l K l, [G:K]) =1, prove that K is unique subgroup of G having order l K l.

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This solution is comprised of a detailed explanation to prove that K is unique subgroup of G having order l K l.

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Let H be a normal subgroup of G with |H| = |K| such that |H|
is relatively prime to [G : K]. We show that H < K, in which case H = K.

To ...

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