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arXiv · 2401.05289

On a fixed point formula of Navarro-Rizo

Benjamin Sambale
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Abstract

Let G be a pi-separable group with a Hall pi-subgroup H or order n. For x in H let lambda(x) be the number of Hall pi-subgroups of G containing x. We show that $\prod_{d\mid n}\prod_{x\in H}\lambda(x^{d})^{\frac{n}{d}\mu(d)}=1$, where mu is the M\"obius function. This generalizes fixed point formulas for coprime actions by Brauer, Wielandt and Navarro-Rizo. We further investigate an additive version of this formula.

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Benjamin Sambale. 2024-01-10. On a fixed point formula of Navarro-Rizo. https://arxiv.org/abs/2401.05289

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