User Tools
definition:symmetric_group
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
|
definition:symmetric_group [2013/08/22 15:49] bmwoodruff |
definition:symmetric_group [2013/08/22 16:47] (current) bmwoodruff |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ====== Symmetric Group ====== | ====== Symmetric Group ====== | ||
| ====Definition==== | ====Definition==== | ||
| - | Let $X$ be any set. The $\textdef{symmetric group}$ on $X$, denoted $\sym(X)$, is the set of all [[permutation]]s of $X$; that is, $\sym(X)$ is the set of all [[wp> | + | Let $X$ be any set. The $\textdef{symmetric group}$ on $X$, denoted $\sym(X)$, is the set of all [[permutation]]s of $X$. We denote by $S_n$ the symmetric group on $X = \{1, |
| Line 17: | Line 17: | ||
| %%%%% | %%%%% | ||
| \begin{definition} | \begin{definition} | ||
| - | Let $X$ be any set. The \textdef{symmetric group} on $X$, denoted $\sym(X)$, is the set of all permutations of $X$; that is, $\sym(X)$ is the set of all bijections from $X$ to $X$. We denote by $S_n$ the symmetric group on $X = \{1, | + | Let $X$ be any set. The \textdef{symmetric group} on $X$, denoted $\sym(X)$, is the set of all permutations of $X$. We denote by $S_n$ the symmetric group on $X = \{1, |
| \end{definition} | \end{definition} | ||
| </ | </ | ||
definition/symmetric_group.1377200954.txt.gz · Last modified: 2013/08/22 15:49 by bmwoodruff
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
