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April 23, 2026Monatshefte für Mathematik0 citationsOpen Access

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

LZLinfeng ZhongJGJidong GuoYYYong Yang

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.

Abstract

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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Cite This Study

Zhong et al. (2026) studied this question.

synapsesocial.com/papers/69e9b9a285696592c86ec4cchttps://doi.org/10.1007/s00605-026-02183-5
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