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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2009 • Question 1

Question

Math 6310 • Algebra Spring 2009 • Question 1

Consider the symmetric group \(S_p\) for \(p\) an odd prime. Let \(C\) be the centralizer of the \(p\)-cycle \(\sigma =(1\ 2\ \ldots \ p)\) and let \(N\) be the normalizer of \(\langle \sigma \rangle \) in \(S_p\). What is the order of each of the groups \(C\) and \(N\)? Are they abelian?

Raw LaTeX

Consider the symmetric group \(S_p\) for \(p\) an odd prime. Let \(C\) be the centralizer of the
\(p\)-cycle \(\sigma=(1\ 2\ \ldots\ p)\) and let \(N\) be the normalizer of \(\langle\sigma\rangle\) in
\(S_p\). What is the order of each of the groups \(C\) and \(N\)? Are they abelian?

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Finite Group Theory Symmetric and Alternating Groups