What question did this study set out to answer?

This paper aims to establish explicit bounds for the degrees of irreducible characters of finite solvable groups.

April 23, 2026Open Access

Character correspondences, degrees and derived length of certain solvable linear groups

Puntos clave

This paper aims to establish explicit bounds for the degrees of irreducible characters of finite solvable groups.
Analyzed character degrees in solvable groups under specific conditions.
Evaluated cases where Sylow 2-subgroups are abelian or |G| is not divisible by 3.
Addressed a conjecture posed by Navarro.
Presented explicit bounds for character degrees in terms of |V|.
Identified different behaviors in groups depending on Sylow 2-subgroup structure.
Contributions advance understanding of character theory in finite groups.

Resumen

Abstract Suppose that G is a finite solvable group, V is a finite faithful completely reducible G -module over a field of characteristic p. In this paper, we first give explicit bounds for the degrees of the irreducible characters of G in terms of | V | in the two cases where 3 |G| 3 ∤ | G | or where the semidirect product GV has abelian Sylow 2-subgroups, respectively. We then use these results to study a conjecture of Navarro.

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