Realizability and tameness of fusion systems

Carlos Broto Blanco, Jesper M. Møller, Bob Oliver, Albert Ruiz Cirera

Producción científica: Otra contribución

Resumen

The fusion system of a finite group at a prime $p$ is a category that encodes all conjugacy relations among subgroups and elements of a given Sylow $p$-subgroup. Such a fusion system is tame if there is some (possibly different) finite group that realizes it, with the property (very approximately) that all automorphisms of the fusion system are induced by automorphisms of the group. In this paper, we prove that all fusion systems of finite groups are tame. This was already known for fusion systems of (known) finite simple groups, and the arguments here consist mainly of a reduction to that case. In particular, this result depends on the classification of finite simple groups.
Idioma originalInglés
DOI
EstadoPublicada - 2 nov 2023

Series de publicaciones

NombreProceedings of the London Mathematical Society
EditorLondon Mathematical Society

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