Work

Characters of relative π′$\pi ^{\prime }$‐degree over normal subgroups

Year: 2025

Type: 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 of the ratios , for irreducible characters of a finite group that lie over a fixed ‐invariant irreducible character of a normal subgroup of , to the structure of Sylow ‐subgroups of . 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 of primes, with a mild condition on if the alternating group is involved in the group.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70361

Authors: Martin W. Liebeck, Gabriel Navarro, Cheryl E. Praeger, Pham Huu Tiep

Institutions: Imperial College London, Universitat de València, The University of Western Australia, Rutgers, The State University of New Jersey

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation, European Regional Development Fund

Awards: Group Representations and Applications, Representations of Finite Groups and Applications, G7925693298, G929308097