My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
October 22nd, 2007, 04:53 PM   #1
Joined: Oct 2007

Posts: 3
Thanks: 0

permutation as a product of factors

Prove 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.
Frazier001 is offline  
October 23rd, 2007, 12:22 AM   #2
Site Founder
julien's Avatar
Joined: Nov 2006
From: France

Posts: 824
Thanks: 7

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).
julien is offline  

  My Math Forum > College Math Forum > Abstract Algebra

factors, permutation, product

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Product of prime factors gazing600000 Calculus 1 April 7th, 2013 08:36 AM
property of numbers of factors of factors of a number mathbalarka Number Theory 15 June 15th, 2012 07:36 PM
Proof on product of cycles (permutation groups) Kappie Abstract Algebra 1 March 13th, 2012 09:30 PM
Product of 4 factors Tartarus Algebra 6 November 26th, 2009 11:31 AM
what is the difference? cartesian product tensor product etc otaniyul Linear Algebra 0 October 30th, 2009 06:40 PM

Copyright © 2019 My Math Forum. All rights reserved.