profile-img
Vijay posted an Question
October 08, 2020 • 12:15 pm 30 points
  • IIT JAM
  • Mathematics (MA)

In the following example, the total number of elements in sigma permutation is 8 but the order of sigma permutation is 6 why?

in the following example the total number of elements in Sigma is 8 but the is 6 why?

1 Answer(s) Answer Now
  • 0 Likes
  • 3 Comments
  • 0 Shares
  • comment-profile-img>
    Deepak singh 1 best-answer

    order of any permutations does not depends on total no. of elements in Sn . for finding order - firstly convert given permutations into disjoint cycles then order of permutation = lcm of length of all disjoint cycles of a permutation.. here order of sigma = lcm{3,2,3} = 6. if any doubt then ask

    eduncle-logo-app

    why does the order of a permutation important?

    eduncle-logo-app

    since permutations are collection of bijective functions , \nwe finds order because let say a given permutation have order 6 this means we have to use 6 times composition to get identity I.e every element in domain mapped to same element in codomain (1 maps to 1 , 2 maps to 2 , .......n maps to n ).

    eduncle-logo-app

    feel free to ask again..

  • comment-profile-img>
    Piyush pachauri

    Order is LCM {3,3,2} =6

    eduncle-logo-app

    but the total number of elements is 8 and not 6, please clear my doubt?

    eduncle-logo-app

    it doesn't matter , how many elements are there , just the cycle decomposition and it's Lcm

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers