Characters of relative π'-degree over normal subgroups
File(s)
Accepted version
Author(s)
Liebeck, Martin
Navarro, Gabriel
Praeger, Cheryl
Tiep, Pham Hu
Type
Journal Article
Abstract
The Gluck–Wolf theorem and its general version [Navarro and Tiep, Annals of Math. 178 (2013), 1135–1171] relate arithmetic properties at a fixed prime 𝑝 of the ratios 𝜒(1)∕𝜆(1), for irreducible characters 𝜒 of a finite group 𝐺 that lie over a fixed 𝐺-invariant irreducible character 𝜆 of a normal subgroup 𝑍 of 𝐺, to the structure of Sylow 𝑝-subgroups of 𝐺∕𝑍. This result constituted a key step towards the recent proof [Malle et al., Annals of Math. 200 (2024), 557–608] of Brauer’s Height Zero Conjecture. In this paper, we prove a further extension of the Gluck–Wolf theorem to sets 𝜋 of primes, with a mild condition on 𝜋 if the alternating group 𝖠 7 is involved in the group.
Date Issued
2025-12-01
Date Acceptance
2025-10-31
Citation
Journal of the London Mathematical Society, 2025, 112 (6)
ISSN
0024-6107
Publisher
Wiley
Journal / Book Title
Journal of the London Mathematical Society
Volume
112
Issue
6
Copyright Statement
© 2025 The Author(s). This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Article Number
e70361
Date Publish Online
2025-11-27