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<p>We study the conditions under which the head characters of a finite solvable group, as defined by I. M. Isaacs, behave well with respect to restriction. We also determine the intersection of the kernels of all head characters of the group. Using G. Navarro’s definition of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak {F}'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="fraktur">F</mi> </mrow> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>-characters, we generalize these results for any saturated formation <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak {F}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">F</mi> </math></EquationSource> </InlineEquation> containing the formation of nilpotent groups.</p>

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On a character correspondence associated to \(\mathfrak {F}\)-projectors

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • María José Felipe,
  • Iris Gilabert,
  • Lucia Sanus

摘要

We study the conditions under which the head characters of a finite solvable group, as defined by I. M. Isaacs, behave well with respect to restriction. We also determine the intersection of the kernels of all head characters of the group. Using G. Navarro’s definition of \(\mathfrak {F}'\) F ′ -characters, we generalize these results for any saturated formation \(\mathfrak {F}\) F containing the formation of nilpotent groups.