Differences

This shows you the differences between two versions of the page.

--- definition:symmetric_group [2013/08/20 09:23]
bmwoodruff [External links]
+++ definition:symmetric_group [2013/08/22 16:47] (current)
bmwoodruff
@@ Line 1: / Line 1: @@
 ====== Symmetric Group ======
 ====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 [[wp>bijection|bijections]] from $X$ to $X$. We denote by $S_n$ the symmetric group on $X = \{1,2,\ldots, n\}$.
+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 $X = \{1,2,\ldots, n\}$.
@@ Line 14: / Line 14: @@
 %%%%%
 % DEPENDENCIES
-% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}
+% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}  \DeclareMathOperator{\sym}{Sym}
 %%%%%
 \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 $X = \{1,2,\ldots, n\}$.
+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 $X = \{1,2,\ldots, n\}$.
 \end{definition}
 </file>
@@ Line 26: / Line 26: @@
-{{tag>definition needsreview rjosh rben}}
+{{tag>definition needsreview rjosh rben ben}}

Abstract Algebra IBL Wiki