On the degrees of irreducible characters fixed by some field automorphism in finite groups

2023/09/11 by Nicola Grittini, Grittini, N. · 1 citation
Computer Science · Mathematics · #20C15 (Primary) 20C33 (Secondary) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2309.05796

openalex publication_date 2023/09/11 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28

Abstract

We prove a variant of the Theorem of Ito-Michler, investigating the properties of finite groups where a prime number p does not divide the degree of any irreducible character left invariant by some Galois automorphism σ of order p.

Cited by

• Height zero characters and Galois automorphisms

Related

• The average character degree and an improvement of the Ito-Michler theorem
• Characters of π'-degree
• A characterization of finite groups by certain Galois conjugacy class of irreducible characters
• Character degrees in principal blocks for distinct primes
• Characters of p'-degree and Thompson's character degree theorem