Prove that if $\displaystyle \Omega=\{1,2,....\}$, then $\displaystyle S_{\Omega}$ is an infinite group.

Let $\displaystyle \sigma:\Omega\to\Omega$. I am guessing I need to define a map but I don't know as what.

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- Oct 4th 2011, 05:38 AMdwsmithInfinite group
Prove that if $\displaystyle \Omega=\{1,2,....\}$, then $\displaystyle S_{\Omega}$ is an infinite group.

Let $\displaystyle \sigma:\Omega\to\Omega$. I am guessing I need to define a map but I don't know as what. - Oct 4th 2011, 03:44 PMNonCommAlgRe: Infinite group
- Oct 4th 2011, 05:38 PMTinybossRe: Infinite group
Or you could note that it contains the transposition (n, n+1) for every natural number n.