# Group Theory Proof Form

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.

I am having trouble with this proof and I need it written in complete proof form and I don't really know how to do it.

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#### Solution Preview

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 ...

#### Solution Summary

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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