Purchase Solution

Permutations : Disjoint Transpositions

Not what you're looking for?

Ask Custom Question

If $ belongs to Sn (where Sn is the symmetric group of degree n), show that $^2 = % if and only if $ is a product of disjoint transpositions.

Purchase this Solution
Solution Summary

A proof involving symmetric groups and disjoint transpositions is provided. The proof is concise.

Solution Preview

Here % should mean the unit 1.

If $ is a product of disjoint transpositions, then $=a1*a2...*ak, where ai are ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Fundamental Mathematics Sample Problems

    The last three elements are even since each of them is the product of two disjoint transpositions. Finally, the eight remaining elements are cyclic permutations of length 3, each of which is the product of two transpositions.

  • Group Theory : Permutation Groups and Even Permutations

    88889 Group Theory : Permutation Groups and Even Permutations Determine which of the following are even permutations: (a) ( 1 2 3 ) (b) ( 1 2 3 4 5 )( 1 2 3 )( 4 5

  • Permutations and Disjoint Cycles

    109237 Permutations and Disjoint Cycles Let b be the permutation (1 2 3)(4 5 6 7)(8 9 10 11 12 13) what is b^99 as a product of disjoint cycles. -I know b^99=b^3 but I'm a little confused on the disjoint cycles part.

  • Permutations as Product of Disjoint Cycles

    87115 Permutations as Product of Disjoint Cycles Modern Algebra Group Theory (LXXIX) Permutation Groups The Orbits and Cycles of Permutations Write the given permutation as the product of disjoint cycles 1 2 3 4 5 6 6 5 4 3 1 2

  • Write each of the following permutations as a product of disjoint cycles.

    Permutations arewriiten as roducts of disjoint cycles. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

  • Composition of cycles

    Find the compostion of the following cycles representing permutations on A = {1,2,3,4,5,6,7,8} Answer as a composition of one or more disjoint cycles.

  • Modern/Abstract Algebra Problem (Group Theory)

    =6 g2 One 3 cycle (123)(4) 2 transpositions (12)(13) 1234->2314 4!/(1*3)=8 g3 One 4 cycle (1234) 3 transpositions (12)(13)(14) 1234->2341 4!

  • Two questions in group theory

    In , the only odd permutations are transpositions, so it follows that xy is a transposition, and thus . Thus xy satisfy all the generator relations for .

  • Conjugacy classes

    Hence, the conjugacy classes in S_4 are: {()} , {the transpositions (ab)}, {double transpositions (ab)(cd)}, {the 3-cycles (abc)} {the 4-cycles (abcd)} (b) One conjugacy class is certainly {()}.

View More Related Solutions