# Sylow p-subgroup

If $(G,*)$ is a group then any subgroup of order $p^{a}$ for any integer a is called a p-subgroup. If $|G|=p^{a}m$, where $p\nmid m$ then any subgroup $S$ of $G$ with $|S|=p^{a}$ is a Sylow p-subgroup. We use ${\rm Syl_{p}}(G)$ for the set of Sylow p-groups of $G$.

More generally, if $G$ is any group (not necessarily finite), a Sylow p-subgroup is a maximal $p$-subgroup of $G$.

 Title Sylow p-subgroup Canonical name SylowPsubgroup Date of creation 2013-03-22 12:50:59 Last modified on 2013-03-22 12:50:59 Owner Henry (455) Last modified by Henry (455) Numerical id 8 Author Henry (455) Entry type Definition Classification msc 20D20 Synonym Sylow subgroup Synonym Sylow group Related topic SylowTheorems Related topic ProofOfSylowTheorems Related topic PPrimaryComponent Related topic SylowsThirdTheorem Defines Sylow p-subgroup Defines p-subgroup