Unformatted text preview: 2. Does there exist a nonabelian group of order 8 with this property? (Justify your answer!) (8 points) 5. Let G be a group and let a ∈ G . Prove that C G ( h a i ) = C G ( { a } ) . (9 points) 6. Let G be a ﬁnite cyclic group and let N ± G . Prove that there exists H ≤ G such that H ∼ = G / N . Does this result remain true without the hypothesis that G is ﬁnite? (8 points) Test on Monday, February 21. Material as far as section 3.3 approximately . One problem will be identical to one of the ungraded homework problems. Review session on Sunday, February 20 at 4:45 p.m. in McBryde 210....
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 Spring '08
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 Math, Algebra, Cyclic group, G. Prove

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