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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2015 • Question 1

Question

Math 6310 • Algebra Spring 2015 • Question 1

Let \(\sigma \) be a 5-cycle in \(S_5\). How many elements of \(S_5\) commute with \(\sigma \)? How many elements of the subgroup \(A_5\) commute with \(\sigma \)? How many conjugacy classes of 5 cycles are there in \(A_5\)?

Raw LaTeX

Let \(\sigma\) be a 5-cycle in \(S_5\). How many elements of \(S_5\) commute with \(\sigma\)? How
many elements of the subgroup \(A_5\) commute with \(\sigma\)? How many conjugacy classes of
5 cycles are there in \(A_5\)?

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups Symmetric and Alternating Groups