Details
| Original language | English |
|---|---|
| Pages (from-to) | 3629-3634 |
| Number of pages | 6 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 152 |
| Issue number | 9 |
| Early online date | 19 Jul 2024 |
| Publication status | Published - Sept 2024 |
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.
Keywords
- coprime action, Fixed points, p-solvable groups, Sylow subgroups, π-separable groups
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics(all)
- Applied Mathematics
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In: Proceedings of the American Mathematical Society, Vol. 152, No. 9, 09.2024, p. 3629-3634.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a fixed point formula of Navarro–Rizo
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2024 by Benjamin Sambale.
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
KW - coprime action
KW - Fixed points
KW - p-solvable groups
KW - Sylow subgroups
KW - π-separable groups
UR - http://www.scopus.com/inward/record.url?scp=85200641106&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2401.05289
DO - 10.48550/arXiv.2401.05289
M3 - Article
AN - SCOPUS:85200641106
VL - 152
SP - 3629
EP - 3634
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 9
ER -