On the pronormality of Hall subgroups.

DOI10.1134/S0037446613010035zbMath1275.20013arXiv1302.0933MaRDI QIDQ359323

Evgeny P. Vdovin, Danila Olegovitch Revin

Publication date: 12 August 2013

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

Full work available at URL: https://arxiv.org/abs/1302.0933

zbMATH Keywords

Hall subgroupsfinite groupspronormal subgroupsHall property \(C_\pi\)

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 (13)

On pronormality and strong pronormality of Hall subgroups ⋮ 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 ⋮ Pronormality and strong pronormality of subgroups. ⋮ On the class of groups with pronormal Hall \(\pi\)-subgroups. ⋮ Equivalence of the existence of nonconjugate and nonisomorphic Hall \(\pi\)-subgroups ⋮ On the heritability of the Sylow -theorem by subgroups ⋮ The existence of pronormal \(\pi\)-Hall subgroups in \(E_\pi\)-groups. ⋮ Pronormality and submaximal \(\mathfrak{X}\)-subgroups on finite groups ⋮ Frattini argument for Hall subgroups. ⋮ Heritability of the property \(\mathcal D_\pi\) by overgroups of \(\pi\)-Hall subgroups in the case where \(2\in\pi\). ⋮ On the pronormality of subgroups of odd index in finite simple groups.

Cites Work

• On the heritability of the property \(D_\pi\) by subgroups.
• A conjugacy criterion for Hall subgroups in finite groups.
• On the number of classes of conjugate Hall subgroups in finite simple groups.
• On the existence of Hall subgroups
• On the Hall \(D_ \pi\)-property for finite groups
• Pronormality of Hall subgroups in finite simple groups.
• Around a conjecture of P. Hall.
• An existence criterion for Hall subgroups of finite groups
• Theorems of Sylow type
• Theorems Like Sylow's
• The {ie210-01}-property in finite simple groups
• Conjugacy of Odd order Hall Subgroups
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