Sylow normalizers and irreducible characters with small cyclotomic field of values

TL;DR

This paper explores the relationship between Sylow normalizers' prime divisors and the degrees of irreducible characters with values in small cyclotomic fields, especially in solvable groups.

Contribution

It establishes a new relation linking Sylow normalizers and character degrees with small cyclotomic fields, with stronger results for solvable groups.

Findings

Relation between prime divisors of Sylow normalizers and character degrees

Stronger relations in solvable groups

Character degrees constrained by small cyclotomic fields

Abstract

In this paper, we prove the existence of a relation between the prime divisors of the order of a Sylow normalizer and the degree of characters having values in some small cyclotomic fields. This relation is stronger when the group is solvable.