st12 - (17 points) 3. Let A 6 = 1 be an abelian group with...

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Math 5125 Wednesday, September 13 Sample First Test no. 2. Answer All Problems. Please Give Explanations For Your Answers. 1. Let G be a group with normal subgroups of index 3 and 5. Prove that there exists a group homomorphism of G onto Z / 15 Z . (16 points) 2. Prove that a group of order 280 cannot be simple.
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Unformatted text preview: (17 points) 3. Let A 6 = 1 be an abelian group with no elements of order 2. Show that there is a group G containing A such that | G : A | = 2 and Z ( G ) = 1. (17 points) Test on Wednesday, September 28. Material sections Chapters 3,4,5,6 approximately....
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