S5 Permutations: Can a & b Create Cycle d?

  • Thread starter Thread starter bokasabi
  • Start date Start date
  • Tags Tags
    Permutations
Click For Summary
SUMMARY

The discussion focuses on whether cycles a (123) and b (12345) can combine to form cycle d (12) within the symmetric group S5. The user has explored various permutations, including aba, ab(a^-1), and bab, but has not yet found a solution. The concept of odd and even permutations is highlighted as a crucial hint for solving the problem.

PREREQUISITES
  • Understanding of symmetric groups, specifically S5
  • Knowledge of cycle notation in permutations
  • Familiarity with odd and even permutations
  • Basic combinatorial techniques for permutation manipulation
NEXT STEPS
  • Study the properties of symmetric groups, focusing on S5
  • Learn about cycle decomposition and its applications in permutations
  • Research the concepts of odd and even permutations in detail
  • Explore advanced permutation algorithms to optimize cycle combinations
USEFUL FOR

Mathematics students, particularly those studying group theory, and anyone interested in combinatorial problems involving permutations.

bokasabi
Messages
4
Reaction score
0

Homework Statement



can cycles a and b create cycle d?
let cycle a = 123
cycle b=12345
cycle d = 12

i.e. can some combination of a and b = d

Homework Equations



only working in S5

The Attempt at a Solution



I have tried various different permutations, 23 over all, things like aba, ab(a^-1), bab, (b^2)a(b^2)
things like this. I am not sure if a solution exists but I have been trying different guesses for hours. I don't want to try 120 times to get it.
 
Physics news on Phys.org
Do you know what odd and even permutations are?
 
Good hint!
 

Similar threads

Multiplying permutation cycles
  • · Replies 3 ·
Replies
3
Views
2K
Two Conjectures about Permutations in ##S_n##
  • · Replies 3 ·
Replies
3
Views
2K
Cycle Decomposition of Permutations
  • · Replies 4 ·
Replies
4
Views
1K
Permutations of taking 2 letters from (a, a, b, c)
  • · Replies 8 ·
Replies
8
Views
2K
Conjugation of Permutations: Finding C for CAC-1 with Same Cycle Structure
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Permutations written as product of 2-cycles
  • · Replies 4 ·
Replies
4
Views
3K
Equality of sums of powers
  • · Replies 47 ·
2
Replies
47
Views
7K
Maximum number of transpositions required to make all permutations.
  • · Replies 1 ·
Replies
1
Views
2K
Proving t a^-1 = b: Permutations & Cycles Homework
  • · Replies 11 ·
Replies
11
Views
4K
Graduate About a natural extension of Collatz conjecture
  • · Replies 3 ·
Replies
3
Views
1K