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--- definition:sylow_p-subgroup [2013/08/08 08:46]
joshuawiscons created
+++ definition:sylow_p-subgroup [2013/08/14 10:08] (current)
bmwoodruff
@@ Line 1: / Line 1: @@
 ====== Sylow $p$-subgroup ======
-**Definition.** Let $G$ be a [[Definition:Group|group]] and $p$ a prime. A [[Definition:p-Group|$p$-subgroup]] $P \le G$ is called a __//Sylow $p$-subgroup//__ of $G$ if $P$ is not properly contained in any other [[Definition:p-group|$p$-subgroup]] of $G$, i.e. $P$ is a maximal $p$-subgroup of $G$.
+====Definition====
+Let $G$ be a [[Definition:Group|group]] and $p$ a prime. A [[Definition:p-Group|$p$-subgroup]] $P \le G$ is called a //Sylow $p$-subgroup// of $G$ if $P$ is not properly contained in any other [[Definition:p-group|$p$-subgroup]] of $G$, i.e. if $P$ is a maximal $p$-subgroup of $G$. The collection of all Sylow $p$-subgroups of $G$ is usually denoted $\textrm{Syl}_p(G)$.
 ----
@@ Line 8: / Line 9: @@
 ----
-==== LaTeX version ====
+==== $\LaTeX$ version ====
 <code>
 %%%%%%%%%%
 % DEPENDENCIES
-% --RequiredMacros: \newcommand{\textDef}[1]{\textit{\underline{#1}}}
+% RequiredMacros: \DeclareMathOperator{\syl}{Syl}
 %%%%%%%%%%
 \begin{definition}
-Let $G$ be a group and $p$ a prime. A $p$-subgroup $P \le G$ is called a \textDef{Sylow $p$-subgroup} of $G$ if $P$ is not properly contained in any other $p$-subgroup of $G$, i.e. $P$ is a maximal $p$-subgroup of $G$.
+Let $G$ be a group and $p$ a prime. A $p$-subgroup $P \le G$ is called a \textit{Sylow $p$-subgroup} of $G$ if $P$ is not properly contained in any other $p$-subgroup of $G$, i.e. if $P$ is a maximal $p$-subgroup of $G$. The collection of all Sylow $p$-subgroups of $G$ is usually denoted $\syl_p(G)$.
 \end{definition}
 </code>

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