# A J\"ordan-Holder type theorem for supercharacter theories

## TL;DR

This paper establishes a Jordan-Hölder type theorem for supercharacter theories of finite groups, extending classical results about group structure to a broader algebraic framework.

## Contribution

It introduces a novel Jordan-Hölder theorem applicable to supercharacter theories, generalizing existing theorems for chief series of finite groups.

## Key findings

- Proves a Jordan-Hölder type theorem for supercharacter theories
- Generalizes classical group structure theorems
- Provides a new tool for analyzing finite groups

## Abstract

The Jordan-H\"older Theorem is a general term given to a collection of theorems about maximal chains in suitably nice lattices. For example, the well-known Jordan-H\"older 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-H\"older type theorem for supercharacter theories of finite groups, which generalizes the one for chief series of finite groups.