A Jördan-Holder type theorem for supercharacter theories

Abstract

The Jordan-Hölder Theorem is a general term given to a collection of theorems about maximal chains in suitably nice lattices. For example, the well-known Jordan-Hölder type theorem for chief series of finite groups has been rather useful in studying the structure of finite groups. In this paper, we present a Jordan-Hölder type theorem for supercharacter theories of finite groups, which generalizes the one for chief series of finite groups.