Nikolaus Conference 2023

Speaker: Edoardo Salati (Dresden)

Title: Large p-Subgroups: a Local Approach


The notion of a large p-subgroup of a finite group first appears in a project initiated by Meierfrankenfeld, Stellmacher and Stroth, whose aim consists in describing all finite groups of local characteristic p. A result central to the project is the structure theorem for finite groups with a large p-subgroup, nearly a classification of the p-local structure of a such a group. We are aiming at a similar structure theorem for mathematical objects that capture only the p-local properties of finite groups, namely for fusion systems and localities. I will talk about analogies and differences with respect to the structure theorem for groups, about our strategy of focusing on localities and the reasons behind this choice and about some results. This is joint work with Ellen Henke.

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