On a fixed point formula of Navarro–Rizo

authored by

Benjamin Sambale

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.

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

Mathematics(all), Applied Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2401.05289 (Access: Open)
https://doi.org/10.1090/proc/16936 (Access: Closed)