Unformatted text preview: Exercise 11. Let G be a ﬁnite group, let H ≤ G and let K C G . Prove that if  H  is relatively prime to [ G : K ] then H ≤ K . [ Hint: Given a ∈ H , by considering the orders of a in H and aK in G/K , show that h a i ≤ K .] Exercise 12. Lang, II.4.30....
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 Spring '10
 RyanDaileda
 Algebra, Sets, Algebraic structure, Homomorphism, Universal algebra, isomorphism theorem

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