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

Key Points

• 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.