Euler characteristics of p-subgroup categories

We compute Euler characteristics of p-subgroup categories of finite groups

💡 Research Summary

The paper investigates the Euler characteristics of three natural categories built from the p‑subgroups of a finite group G: the poset 𝒮_G(p) of all p‑subgroups ordered by inclusion, the transport category 𝒯_G(p) that identifies subgroups up to G‑conjugacy, and the fusion (or “transporter”) category ℱ_G(p) whose morphisms are group elements effecting conjugation from one p‑subgroup to another. The authors adopt the framework of Möbius inversion on finite categories: for any finite category 𝒞 one can define a Möbius function μ on its objects, a weighting w and a coweighting v satisfying
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