π-separable group

Let π be a set of prime numbersMathworldPlanetmath. A finite groupMathworldPlanetmath G is called π-separablePlanetmathPlanetmath if there exists a composition seriesMathworldPlanetmathPlanetmath


such that each Gi+1/Gi is either a π-group (http://planetmath.org/PiGroupsAndPiGroups) or a π-group (http://planetmath.org/PiGroupsAndPiGroups).

A {p}-separable group, where p is a prime number, is usually called a p-separable group.

π-separability can be thought of as a generalizationPlanetmathPlanetmath of solvability for finite groups; a finite group is π-separable for all sets of primes if and only it is solvable.

Title π-separable group
Canonical name piseparableGroup
Date of creation 2013-03-22 13:17:48
Last modified on 2013-03-22 13:17:48
Owner yark (2760)
Last modified by yark (2760)
Numerical id 7
Author yark (2760)
Entry type Definition
Classification msc 20D10
Defines π-separable
Defines p-separable
Defines π-separability
Defines p-separability
Defines p-separable group