Unformatted text preview: (3 points) 3. Let G be a group, and suppose there is a homomorphism of G onto S 3 (the symmetric group of degree 3) with kernel K . Determine the number of subgroups of G which contain K , and show that exactly three of these subgroups are normal. (3 points) 4. Section 3.5, Exercise 2 on page 111. (2 points) 5. Section 4.1, Exercise 5(a) on page 116. (3 points) (5 problems, 14 points altogether)...
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 Spring '08
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 Math, Algebra, Group Theory, Normal subgroup, Prove

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