The square of a permutation is even

Prove that \sigma^2 is an even permutation for all \sigma.


Let \epsilon denote the sign homomorphism S_n \rightarrow Z_2. We have \epsilon(\sigma^2) = \epsilon(\sigma)^2 = 1, so that \sigma^2 is even for all \sigma.

Advertisements
Post a comment or leave a trackback: Trackback URL.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: