Paper 3, Section I, E

Groups | Part IA, 2012

What is a cycle in the symmetric group SnS_{n} ? Show that a cycle of length pp and a cycle of length qq in SnS_{n} are conjugate if and only if p=qp=q.

Suppose that pp is odd. Show that any two pp-cycles in Ap+2A_{p+2} are conjugate. Are any two 3 -cycles in A4A_{4} conjugate? Justify your answer.

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