Let G be a finite groupMathworldPlanetmath with order n, and let p be a prime integer. We can write n=pkm for some k,m integers, such that k and m are coprimesMathworldPlanetmath (that is, pk is the highest power of p that divides n). Any subgroupMathworldPlanetmathPlanetmath of G whose order is pk is called a Sylow p-subgroup.

While there is no reason for Sylow p-subgroups to exist for any finite group, the fact is that all groups have Sylow p-subgroups for every prime p that divides |G|. This statement is the First Sylow theoremMathworldPlanetmath

When |G|=pk we simply say that G is a p-group.

Title p-subgroup
Canonical name Psubgroup
Date of creation 2013-03-22 14:02:14
Last modified on 2013-03-22 14:02:14
Owner drini (3)
Last modified by drini (3)
Numerical id 8
Author drini (3)
Entry type Definition
Classification msc 20D20
Related topic PGroup4
Defines Sylow p-subgroup
Defines Sylow p-subgroupMathworldPlanetmathPlanetmath
Defines p-group
Defines p-groupMathworldPlanetmathPlanetmath