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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.

    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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    https://brainmass.com/math/group-theory/group-theory-proof-form-212645

    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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