On the partial $Π$-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

Let $H$ be a subgroup of a finite group $G$ . We say that $H$ satisfies the partial $Π$ -property in $G$ if if there exists a chief series $Γ_{G} : 1 = G_{0} < G_{1} < \cdot \cdot \cdot < G_{n} = G$ of $G$ such that for every $G$ -chief factor $G_{i} / G_{i - 1}$ $(1 \leq i \leq n)$ of $Γ_{G}$ , $∣ G / G_{i - 1} : N_{G / G_{i - 1}} (H G_{i - 1} / G_{i - 1} \cap G_{i} / G_{i - 1}) ∣$ is a $π (H G_{i - 1} / G_{i - 1} \cap G_{i} / G_{i - 1})$ -number. In this paper, we study the influence of some second minimal or second maximal subgroups of a Sylow subgroup satisfying the partial $Π$ -property on the structure of a finite group.

On the partial $Π$ -property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

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On the partial $Π$ -property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

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On the partial ΠΠ-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

文献摘要

讨论

|讲解博客

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On the partial ΠΠ-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

文献摘要

讨论

|讲解博客

|AI智能校验

On the partial $Π$ -property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

讲解博客

AI智能校验

On the partial $Π$ -property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

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