Schreier refinement theorem

The Schreier Refinement Theorem states that any two subnormal series for a group have equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath refinementsMathworldPlanetmathPlanetmath. Here, two subnormal series are considered equivalent if they have the same factors (up to isomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath), not necessarily in the same order.

This theorem can be used to prove the Jordan-Hölder Theorem (, and can also be used to prove that the Hirsch number of a polycyclic group is well-defined.

Title Schreier refinement theorem
Canonical name SchreierRefinementTheorem
Date of creation 2013-03-22 14:40:53
Last modified on 2013-03-22 14:40:53
Owner yark (2760)
Last modified by yark (2760)
Numerical id 8
Author yark (2760)
Entry type Theorem
Classification msc 20E15