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OpenStudy (anonymous):
Let |G| = n < ∞, H be a subgroup of G, and assume that the number n does not divide the factorial of the index of H in G. Prove that there exists a normal subgroup N not equal {e} of G contained in H.
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OpenStudy (anonymous):
(Hint: Consider the natural left action of the group G on the left coset space X = G/H.)
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