home3 - 4 Problem 2.6#12 5 Problem 2.7#4 Note You can...

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MATH 4107 HOMEWORK #3 DUE: March 5, 2010 Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for grading. Write LEGIBLY on the FRONT side of the page only, and STAPLE your pages together. 1. Problem 2.6 #3. Note: I worked out this problem in class, but I want you to give a complete proof. 2. Problem 2.6 #4. 3. Problem 2.6 #5.
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Unformatted text preview: 4. Problem 2.6 #12. 5. Problem 2.7 #4. Note: You can assume without proof that G 1 × G 2 is a group. Hint for (c): Find a function that maps G 1 × G 2 to G 2 , and then use the First Homomor-phism Theorem. 6. Problem 2.7 #5. I will give some discussion and hints on this problem in class. Note for (a): You can assume without proof that H ∩ N is a subgroup, just prove it is normal. Note that you have to prove it is normal in H , not in G ! 1...
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This note was uploaded on 08/25/2011 for the course MATH 4107 taught by Professor Staff during the Spring '10 term at University of Florida.

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