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Abstract <p> Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak N\subseteq \mathfrak F\subseteq \mathfrak D\)</EquationSource> </InlineEquation>, let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak F\)</EquationSource> </InlineEquation> be a saturated subgroup-closed formation, and let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak N\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak D\)</EquationSource> </InlineEquation> be the formations of all nilpotent and all Ore dispersive finite groups, respectively. Sufficient conditions are obtained for a finite group to belong to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathfrak F\)</EquationSource> </InlineEquation> under the condition that the normalizers of all Sylow subgroups are contained in <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathfrak F\)</EquationSource> </InlineEquation>. </p>

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Finite Groups with Dispersive Sylow Normalizers

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • V. S. Monakhov

摘要

Abstract

Let \(\mathfrak N\subseteq \mathfrak F\subseteq \mathfrak D\) , let \(\mathfrak F\) be a saturated subgroup-closed formation, and let \(\mathfrak N\) and \(\mathfrak D\) be the formations of all nilpotent and all Ore dispersive finite groups, respectively. Sufficient conditions are obtained for a finite group to belong to \(\mathfrak F\) under the condition that the normalizers of all Sylow subgroups are contained in \(\mathfrak F\) .