π-groups and π-groups

Let π be a set of primes. A torsion groupPlanetmathPlanetmath G is called a π-group if each prime dividing the order of an element of G is in π and a π-group if none of them are. Typically, if π is a singleton π={p}, we write p-group and p-group for these.

Remark. If G is finite, then G is a π-group if every prime dividing |G| is in π.

Title π-groups and π-groups
Canonical name pigroupsAndpigroups
Date of creation 2013-03-22 13:17:51
Last modified on 2013-03-22 13:17:51
Owner Algeboy (12884)
Last modified by Algeboy (12884)
Numerical id 9
Author Algeboy (12884)
Entry type Definition
Classification msc 20D20
Classification msc 20F50
Defines π-group
Defines π-group