The existence of pronormal \(\pi\)-Hall subgroups in \(E_\pi\)-groups.

DOI10.1134/S0037446615030015zbMath1325.20017arXiv1504.02834MaRDI QIDQ498223

Danila Olegovitch Revin, Evgeny P. Vdovin

Publication date: 28 September 2015

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.02834

zbMATH Keywords

Hall subgroupsfinite groupspronormal subgroupsFrattini argumentHall \(E_\pi\)-property

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Special subgroups (Frattini, Fitting, etc.) (20D25) Subnormal subgroups of abstract finite groups (20D35)

Related Items (8)

On pronormality and strong pronormality of Hall subgroups ⋮ On the pronormality of subgroups of odd index in some direct products of finite groups ⋮ Abnormality criteria for \(p\)-complements ⋮ Pronormality of Hall subgroups in their normal closure ⋮ Classification and properties of the \(\pi \)-submaximal subgroups in minimal nonsolvable groups ⋮ Equivalence of the existence of nonconjugate and nonisomorphic Hall \(\pi\)-subgroups ⋮ On the heritability of the Sylow -theorem by subgroups ⋮ Pronormality and submaximal \(\mathfrak{X}\)-subgroups on finite groups

Cites Work

• Unnamed Item
• On the pronormality of Hall subgroups.
• On the class of groups with pronormal Hall \(\pi\)-subgroups.
• A conjugacy criterion for Hall subgroups in finite groups.
• On the number of classes of conjugate Hall subgroups in finite simple groups.
• Frattini argument for Hall subgroups.
• Pronormality of Hall subgroups in finite simple groups.
• Hall \(\pi\)-subgroups of finite Chevalley groups whose characteristic belongs to \(\pi\)
• An existence criterion for Hall subgroups of finite groups
• Theorems of Sylow type
• Theorems Like Sylow's

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