# Groups with one or two super-Brauer character theories

## TL;DR

This paper classifies finite groups based on the number of super-Brauer character theories they possess, focusing on groups with exactly one or two such theories, advancing understanding in modular representation theory.

## Contribution

It provides a complete classification of groups with exactly one or two super-Brauer character theories, a novel result in the study of modular characters.

## Key findings

- Groups with exactly one super-Brauer character theory are characterized.
- Classification of groups with exactly two super-Brauer character theories is discussed.

## Abstract

A super-Brauer character theory of a group $G$ and a prime $p$ is a pair consisting of a partition of the irreducible $p$-Brauer characters and a partition of the $p$-regular elements of $G$ that satisfy certain properties. We classify the groups and primes that have exactly one super-Brauer character theory. We discuss the groups with exactly two super-Brauer character theories.