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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.05289 |
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| _version_ | 1866911754079961088 |
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| author | Sambale, Benjamin |
| author_facet | Sambale, Benjamin |
| contents | 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 $\prod_{d\mid n}\prod_{x\in H}λ(x^{d})^{\frac{n}{d}μ(d)}=1$, where mu is the Möbius function. This generalizes fixed point formulas for coprime actions by Brauer, Wielandt and Navarro-Rizo. We further investigate an additive version of this formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a fixed point formula of Navarro-Rizo Sambale, Benjamin Group Theory 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 $\prod_{d\mid n}\prod_{x\in H}λ(x^{d})^{\frac{n}{d}μ(d)}=1$, where mu is the Möbius function. This generalizes fixed point formulas for coprime actions by Brauer, Wielandt and Navarro-Rizo. We further investigate an additive version of this formula. |
| title | On a fixed point formula of Navarro-Rizo |
| topic | Group Theory |
| url | https://arxiv.org/abs/2401.05289 |