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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online