Corpus ID: 235694471

Some products in fusion systems and localities

@inproceedings{Henke2021SomePI,
  title={Some products in fusion systems and localities},
  author={Ellen Henke},
  year={2021}
}
The theory of saturated fusion systems resembles in many parts the theory of finite groups. However, some concepts from finite group theory are difficult to translate to fusion systems. For example, products of normal subsystems with other subsystems are only defined in special cases. In this paper the theory of localities is used to prove the following result: Suppose F is a saturated fusion system over a p-group S. If E is a normal subsystem of F over T ≤ S, and D is a normal subsystem of NF… Expand
1 Citations
Kernels of Localities
We state a sufficient condition for a fusion system to be saturated. This is then used to investigate localities with kernels, i.e. localities which are (in a particular way) extensions of groups byExpand

References

SHOWING 1-10 OF 13 REFERENCES
Normal subsystems of fusion systems
In this article, we prove that, for any saturated fusion system, the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety ofExpand
The Generalized Fitting Subsystem of a Fusion System
The notion of a fusion system was first defined and explored by Puig, in the context of modular representation theory. Later, Broto, Levi, and Oliver extended the theory and used it as a tool inExpand
Fusion Systems in Algebra and Topology
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 axioms first formulatedExpand
The homotopy theory of fusion systems
The main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p-completed classifying spaces of finite groups. These spaces occur as the “classifyingExpand
Fusion systems and localities
We introduce objective partial groups, of which the linking systems and p-local finite groups of Broto, Levi, and Oliver, the transporter systems of Oliver and Ventura, and theExpand
Subcentric linking systems
Linking systems are crucial for studying the homotopy theory of fusion systems, but are also of interest from an algebraic point of view. We propose a definition of a linking system associated to aExpand
Extensions of linking systems with p-group kernel
We study extensions of p-local finite groups where the kernel is a p-group. In particular, we construct examples of saturated fusion systems $${\mathcal{F}}$$ which do not come from finite groups,Expand
Subgroup Families Controlling p‐Local Finite Groups
A $p$-local finite group consists of a finite $p$-group $S$, together with a pair of categories which encode ?conjugacy? relations among subgroups of $S$, and which are modelled on the fusion in aExpand
Extensions of linking systems and fusion systems
We correct two errors in the statement and proof of a theorem in an earlier paper (2007), and at the same time extend that result to a more general theorem about extensions of p-local finite groups.Expand
Products in fusion systems
Abstract We revisit the notion of a product of a normal subsystem with a p -subgroup as defined by Aschbacher (2011) [Asc11, Chapter 8] . In particular, we give a previously unknown, more transparentExpand
...
1
2
...