st13 - B = C . (17 points) 3. Let F be a nonabelian free...

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Math 5125 Wednesday, September 21 Sample First Test no. 3. Answer All Problems. Please Give Explanations For Your Answers. 1. Let p be a prime, let n be a positive integer, and let G be a noncyclic group of order p n . Prove that there exists K ± G such that G / K is abelian and noncyclic. (Use induction on | G | .) (17 points) 2. Let A , B , C be finitely generated abelian groups. Prove that if A × B = A × C , then
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Unformatted text preview: B = C . (17 points) 3. Let F be a nonabelian free group. Prove that Z ( F ) = 1. (16 points) Test on Wednesday, September 28. Material most of Chapters 3,4,5 and Section 6.3. One of the problems will be identical to one of the ungraded homework problems and one of the problems will be identical to one of the sample test problems....
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