Realizability and tameness of fusion systems

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

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Resum

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 originalEnglish
DOIs
Estat de la publicacióPublicada - 2 de nov. 2023

Sèrie de publicacions

NomProceedings of the London Mathematical Society
EditorLondon Mathematical Society

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