Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

let $\pi$ be a transposition in permutation group $S_n$ that $n>1$. Is the centralizer of $\pi$ on $S_n$ i.e $C_{S_n}(\pi)$ isomorphic with $\mathbb Z_2\times S_{n-2}$ or $\mathbb Z_2\times S_{n-1}$?

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

Hint: Assume for convenience that $\pi$ is the permutation $(1 \ 2)$. Show that if $\sigma \in S_n$ satisfies $\sigma(1) \notin \{1, 2\}$ or $\sigma(2) \notin \{1, 2\}$ then $\sigma$ does not commute with $\pi$.

share|improve this answer
    
@ Jim please explain more –  rese Mar 11 '13 at 19:30
    
A permutation $\sigma$ is in the centralizer of $(1 \ 2)$ if and only if $\sigma(1), \sigma(2) \in \{1, 2\}$. –  Jim Mar 11 '13 at 20:56
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.