Abstract Algebra IBL Wiki

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.

====== Permutation Group ======
====Definition==== 
A $\textdef{permutation group}$ on $X$ is a set of [[definition:permutation]]s of $X$ that contains the identity permutation and is closed under function composition and taking inverses.

----
==== Remarks ==== 
  * Alternately, a permutation group is a subgroup of $\sym{X}$, where $\sym{X}$ denotes the [[definition:symmetric group]] on $X$.


----
==== $\LaTeX$ version ====
<file tex definition.permutation_group.tex>
%%%%%
% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}
%%%%%
\begin{definition}
A \textdef{permutation group} on $X$ is a set of permutations of $X$ that contains the identity permutation and is closed under function composition and taking inverses.
\end{definition}
</file>

----
==== External links ====
  * [[wp>Permutation group]]


{{tag>definition needsreview rben ben rjosh}}

Abstract Algebra IBL Wiki

User Tools

Site Tools

Page Tools