Can a permutation with non-disjoint cycles still be used to find its order?

  • Context: Undergrad 
  • Thread starter Thread starter physix123
  • Start date Start date
  • Tags Tags
    Cycles
Click For Summary
SUMMARY

To determine the order of a permutation, the method of finding the least common multiple (LCM) of the lengths of disjoint cycles is valid. However, for permutations with non-disjoint cycles, such as (1,3,6,8)(4,6), this method does not apply directly. Instead, one must first rewrite the permutation into a single cycle representation to accurately compute its order. This involves identifying the complete cycle structure of the permutation.

PREREQUISITES
  • Understanding of permutation notation and cycle representation
  • Knowledge of least common multiple (LCM) calculations
  • Familiarity with cycle decomposition in group theory
  • Experience with non-disjoint cycle examples in permutations
NEXT STEPS
  • Study cycle decomposition techniques for permutations
  • Learn how to compute the order of permutations with non-disjoint cycles
  • Explore examples of permutations and their cycle structures
  • Investigate the properties of LCM in relation to group theory
USEFUL FOR

Mathematicians, computer scientists, and students studying group theory or combinatorics, particularly those interested in permutation analysis and cycle structures.

physix123
Messages
3
Reaction score
0
i am pretty sure it's true that to find the order of a permutation, you can find LCM of the length of the disjoint cycles...

if you have a permutation that doesn't have disjoint cycles (i.e. like one with (1,3,6,8)(4,6)), then can you use the same method to find the order? I feel like I am missing something...
 
Physics news on Phys.org
Rewrite (1,3,6,8)(4,6) as one permutation.
 

Similar threads

Undergrad Order of a permutation is the lcm of the orders of cycles
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Modern Algebra: Permutations and Cycles
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad When is D_{n} abelian? What's wrong with the proof?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Differences between left vs right actions in some group theory questions
  • · Replies 1 ·
Replies
1
Views
817
Multiplying permutation cycles
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Counting cycles in a permutation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Multiplying non-disjoint permutation cycles
  • · Replies 3 ·
Replies
3
Views
24K
Graduate How to find the number of elements with a particular order in a group?
  • · Replies 1 ·
Replies
1
Views
5K
Two Conjectures about Permutations in ##S_n##
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Prove Even # Transpositions in Identity Permutation w/ Induction & Contradiction
  • · Replies 8 ·
Replies
8
Views
5K