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--- definition:sylow_p-subgroup [2013/08/09 05:12]
joshuawiscons
+++ 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. if $P$ is a maximal $p$-subgroup of $G$. The collection of all Sylow $p$-subgroups of $G$ is usually denoted $\textrm{Syl}_p(G)$.
+====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 $\textrm{Syl}_p(G)$.
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