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<p>In this paper, we are interested in the real-valued strongly monolithic characters of finite groups. We give some criteria for solvability and normal <i>p</i>-complements of finite groups by their real-valued strongly monolithic characters. We also prove that a finite nonsolvable group has a real-valued strongly monolithic character of degree <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\geqslant 5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>⩾</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>. Additionally, we give a classification for odd-square-free groups by using their real-valued strongly monolithic characters and the zeros of their irreducible characters of odd degree.</p>

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Real strongly monolithic characters of finite groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月29日

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  • Temha Erkoç,
  • Ömer Demir

摘要

In this paper, we are interested in the real-valued strongly monolithic characters of finite groups. We give some criteria for solvability and normal p-complements of finite groups by their real-valued strongly monolithic characters. We also prove that a finite nonsolvable group has a real-valued strongly monolithic character of degree \(\geqslant 5\) ⩾ 5 . Additionally, we give a classification for odd-square-free groups by using their real-valued strongly monolithic characters and the zeros of their irreducible characters of odd degree.