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.© BrainMass Inc. brainmass.com October 9, 2019, 10:13 pm ad1c9bdddf
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.
This solution is comprised of a detailed explanation to prove that K is unique subgroup of G having order l K l.