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composition of permutations

Source: IMC 1998 day 1 problem 2

November 1, 2005
geometrygeometric transformationrotationsuperior algebrasuperior algebra unsolved

Problem Statement

Consider the following statement: for any permutation π1≠I\pi_1\not=\mathbb{I} of {1,2,...,n}\{1,2,...,n\} there is a permutation π2\pi_2 such that any permutation on these numbers can be obtained by a finite compostion of π1\pi_1 and π2\pi_2. (a) Prove the statement for n=3n=3 and n=5n=5. (b) Disprove the statement for n=4n=4.
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