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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2011 • Question 1

Question

Math 6310 • Algebra Spring 2011 • Question 1

Let \(p\) be a prime. Show that an element in the symmetric group \(S_n\) has order \(p\) if and only if it is a product of commuting \(p\)-cycles. Show by an explicit example that this need not be the case if \(p\) is not prime.

Raw LaTeX

Let \(p\) be a prime. Show that an element in the symmetric group \(S_n\) has order \(p\) if and
only if it is a product of commuting \(p\)-cycles. Show by an explicit example that this need
not be the case if \(p\) is not prime.

Topic Tags

Symmetric and Alternating Groups Tensor Products of Modules