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Name: Problem Set 6 Math 416, Section 500, Spring 2014 Due: Tuesday, March 18th. Review Sections 37 and 38 in your textbook. Complete the following items, staple this page to the front of your work, and turn your assignment in at the beginning of class on Tuesday, March 18th. Remember to fully justify all your answers, and provide complete details. 1. Read Example 37.15. Show that every group of order 5 · 7 · 47 is abelian and cyclic. 2. Read Examples 37.11-37.14. Show that no group of order 96 is simple. 3. a. Determine whether {(2, 1), (3, 1)} is a basis for Z × Z. b. Determine whether {(2, 1), (4, 1)} is a basis for Z × Z. 4. Let G and G0 be free abelian groups. Show that G × G0 is also free abelian. 5. Read the proof of Theorem 38.11 in the book. Now prove Theorem 38.11 in your own words. 6. Extra Credit. Let G be a finitely generated abelian group. Show that G is a free abelian group if and only if G contains no nonzero elements of finite order. Through the course of this assignment, I have followed the Aggie Code of Honor. An Aggie does not lie, cheat or steal or tolerate those who do. Signed: Page 1