- **Abstract Algebra**
(*http://mymathforum.com/abstract-algebra/*)

- - **permutation as a product of factors**
(*http://mymathforum.com/abstract-algebra/1503-permutation-product-factors.html*)

permutation as a product of factorsProve that all permutions in Sn can be produced as products using only the factors sigma=(1 2) and tau=(1 2 3 ... n). Note that tau^-1= tau^n-1. |

The set of all permutations in Sn is generated by the set of all transpositions of S_n. It is therefore enough to prove that any transposition can be generated by the elements (permutations) (1,2) and (1,...,n). Well, for any transposition (i,j), we have (i,j)=(1,...,n)^(j-2+n)(1,2)(1,...,n)^(n-i+1), which solves the problem (provided I didnt do any computational mistake, but the method is correct anyhow). |

All times are GMT -8. The time now is 01:28 PM. |

Copyright © 2019 My Math Forum. All rights reserved.