Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 26 min ago
PreprintarXiv licencearXiv

Gallagher's Theorem for Real-valued Brauer Characters

  • Daryl Zane Adriano
Open at sourcePDFDOICite

Abstract

Let G be a finite group, let N be a normal subgroup of G, and let θ be an irreducible p-Brauer character of N, for a prime p. It is well known that the number of irreducible Brauer characters of G lying over θ equals the number of p-regular θ-good conjugacy classes of Gθ/N. In this note we express the number of real-valued irreducible Brauer characters of G lying over θ in terms of the p-regular θ-good conjugacy classes of Gθ/N. This is a modular analogue of one of the main results in a recent paper (arXiv:2301.01177) by John Murray.

Related

  1. Upper Bounds on the de Bruijn-Newman constant for Dirichlet L-functions with primitive real-valued characters
    Ricardo Freire, Cristian González-Riquelme, Claudio Muñoz +2
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  2. The Brauer A(∞) condition and Navarro's conjecture on Brauer characters under coprime actions
    Zhicheng Feng, Lin Wu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Inhomogeneous Fiber Refinement of Gallagher's Theorem
    Qian Li, Bo Tan, Qing-Long Zhou
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Lifts of Brauer characters and vertex pairs for odd primes
    Yong Yang
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  5. Infinitary real-valued logic and a refinement of the Kochen-Specker theorem
    Olivia Aubone, José Iovino
    arXivPreprintCC BY 4.0Full textLogic & foundationsarXiv

Cite

BibTeXRIS
BibTeX
@misc{adriano2026gallaghers,
  title = {{Gallagher's Theorem for Real-valued Brauer Characters}},
  author = {Daryl Zane Adriano},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00298},
  eprint = {2609.00298},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00298},
}
RIS
TY  - UNPB
TI  - Gallagher's Theorem for Real-valued Brauer Characters
AU  - Daryl Zane Adriano
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00298
UR  - https://arxiv.org/abs/2609.00298
AB  - Let G be a finite group, let N be a normal subgroup of G, and let θ be an irreducible p-Brauer character of N, for a prime p. It is well known that the number of irreducible Brauer characters of G lying over θ equals the number of p-regular θ-good conjugacy classes of G_θ/N. In this note we express the number of real-valued irreducible Brauer characters of G lying over θ in terms of the p-regular θ-good conjugacy classes of G_θ/N. This is a modular analogue of one of the main results in a recent paper (arXiv:2301.01177) by John Murray.
ER  -