Publication details
On a fixed point formula of Navarro–Rizo
Abstract
Let G be a π-separable group with a Hall π-subgroup H or order n. For x ∈ H let λ(x) be the number of Hall π-subgroups of G containing x. We show that Πd|nΠx∈H λ(xd) nd μ(d) = 1, where μ 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.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Proceedings of the American Mathematical Society
- Volume
- 152
- Pages
- 3629-3634
- No. of pages
- 6
- ISSN
- 0002-9939
- Publication date
- 09.2024
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- General Mathematics, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2401.05289 (Access:
Open
)
https://doi.org/10.1090/proc/16936 (Access: Closed )
