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<p>Suppose that <i>G</i> is a finite solvable group, <i>V</i> is a finite faithful completely reducible <i>G</i>-module over a field of characteristic <i>p</i>. In this paper, we first give explicit bounds for the degrees of the irreducible characters of <i>G</i> in terms of |<i>V</i>| in the two cases where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(3\not \mid |G|\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>∤</mo> <mo stretchy="false">|</mo> <mi>G</mi> <mo stretchy="false">|</mo> </mrow> </math></EquationSource> </InlineEquation> or where the semidirect product <i>GV</i> has abelian Sylow 2-subgroups, respectively. We then use these results to study a conjecture of Navarro.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月21日

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  • Linfeng Zhong,
  • Jidong Guo,
  • Yong Yang

摘要

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 \(3\not \mid |G|\) 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.