Unformatted text preview: H ≤ G . Prove that G/H is abelian. Exercise 8. Show that Q / Z is inﬁnite, but that every element in it has ﬁnite order. Exercise 9. Suppose that G = h a i is a cyclic group and H ≤ G . Prove that G/H is cyclic. What is it generated by? [ Suggestion: Use the canonical surjection f : G → G/H and exercise 5b from homework 4.]...
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This note was uploaded on 02/29/2012 for the course MATH 3362 taught by Professor Ryandaileda during the Spring '10 term at Trinity University.
 Spring '10
 RyanDaileda
 Algebra

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