Homework Help: Algebra, permutations.

1. Feb 9, 2014

decerto

1. The problem statement, all variables and given/known data

Suppose σ is an element of S_n, if σ^5=1, is σ necessarily odd or even

2. Relevant equations

$Parity(\sigma)= (\sum_{i=1}^k(|c_i|-1)) mod 2$

3. The attempt at a solution

Really unsure how to even start this, I think I have to use the fact you can decompose every permutation into a product of disjoint or 2 cycles and use their properties to show in what cases it's even or odd but I'm not really sure.

2. Feb 9, 2014

Dick

$\sigma^5=\sigma \sigma \sigma \sigma \sigma=1$. $1$ is an even permutation. Suppose $\sigma$ were odd. Then what would be the parity of $\sigma^5$?

3. Feb 9, 2014

kduna

What does σ5 being even tell you?

Last edited: Feb 9, 2014