Abstract

Saturated fusion systems are categories satisfying important features of fusion in finite groups. They have been studied by algebraic topologists, modular representation theorists and recently also by local group theorists. Many concepts and results from finite group theory have been translated into the language of fusion systems. This makes it possible to attempt a classification of certain classes of saturated fusion systems.

We will define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can be seen as an analog of Thompson’s N-groups whose classification set a pattern for the classification of finite simple groups. I will report on the current progress of a project, which aims to investigate minimal fusion systems for arbitrary primes and to classify minimal fusion systems over $2$-groups.