Editing Schreier refinement theorem (section)

{{Short description|Statement in group theory}}
In [[mathematics]], the '''Schreier refinement theorem''' of [[group theory]] states that any two [[subnormal series]] of [[subgroup]]s of a given group have equivalent refinements, where two series are equivalent if there is a [[bijection]] between their [[factor group]]s that sends each factor group to an [[group isomorphism|isomorphic]] one.

The theorem is named after the [[Austria]]n [[mathematician]] [[Otto Schreier]] who proved it in 1928. It provides an elegant proof of the [[Jordan–Hölder theorem]]. It is often proved using the [[Zassenhaus lemma]]. {{harvtxt|Baumslag|2006}} gives a short proof by intersecting the terms in one subnormal series with those in the other series.