Group With Operators - Applications

Applications

The Jordan–Hölder theorem also holds in the context of operator groups. The requirement that a group have a composition series is analogous to that of compactness in topology, and can sometimes be too strong a requirement. It is natural to talk about "compactness relative to a set", i.e. talk about composition series where each (normal) subgroup is an operator-subgroup relative to the operator set X, of the group in question.