A fusion system over a p-group S is a category whose objects form the set of all subgroups
of S, whose morphisms are certain injective group homomorphisms, and which satisfies …

Fusion systems are a recent development in finite group theory and sit at the intersection of
algebra and topology. This book is the first to deal comprehensively with this new and …

This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of
finite quasi-simple groups by finding the so-called quasi-isolated blocks of exceptional …

Fusion systems were introduced by L. Puig in the early 1990's as a common framework for
fusion systems of finite groups or p-blocks of finite groups. Benson [3] suggested that every …

This is a survey article on the theory of fusion systems, a relatively new area of mathematics
with connections to local finite group theory, algebraic topology, and modular representation …

We prove Erdmann's conjecture (J Algebra 76: 505–518, 1982) stating that every block with
a Klein four defect group has a simple module with trivial source, and deduce from this that …

Let k be an algebraically closed field of characteristic p and G a finite group. An interesting
question for fusion systems is whether they can be obtained from the local structure of a …

We introduce a notion of simple fusion systems which imitates the corresponding notion for
finite groups and show that the fusion system on the Sylow-2-subgroup of a 7-dimensional …

We prove the conjecture that exotic and block-exotic fusion systems coincide holds for all
fusion systems on exceptional p-groups of maximal nilpotency class, where p≥ 5. This is …

Given a fusion system ℱ on a finite p‐group P, where p is a prime, we show that the partially
ordered set of isomorphism classes in ℱ of chains of non‐trivial subgroups of P, considered …