On the Hall \(D_ \pi\)-property for finite groups

DOI10.1007/BF02674906zbMath0880.20012MaRDI QIDQ1375040

Victor D. Mazurov, Danila Olegovitch Revin

Publication date: 5 January 1998

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

zbMATH Keywords

Hall subgroupsfinite groupsSylow subgroups

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Automorphisms of abstract finite groups (20D45) Extensions, wreath products, and other compositions of groups (20E22)

Related Items (14)

The reduction theorem for relatively maximal subgroups ⋮ On intersections of \(\pi \)-Hall subgroups in finite \(D_{\pi} \)-groups ⋮ On the pronormality of Hall subgroups. ⋮ On the class of groups with pronormal Hall \(\pi\)-subgroups. ⋮ Nonabelian composition factors of a finite group whose all maximal subgroups are Hall. ⋮ On a relation between the Sylow and Baer-Suzuki theorems. ⋮ A characterization of finite \(D_\pi\)-groups. ⋮ Conjugacy of maximal and submaximal \(\mathfrak{X}\)-subgroups ⋮ On Baer-Suzuki \(\pi\)-theorems. ⋮ Frattini argument for Hall subgroups. ⋮ The \(D_\pi\) property of finite groups in the case \(2\notin\pi\). ⋮ Formations of finite $C_\pi $-groups ⋮ Heritability of the property \(\mathcal D_\pi\) by overgroups of \(\pi\)-Hall subgroups in the case where \(2\in\pi\). ⋮ Confirmation for Wielandt's conjecture.

Cites Work

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• Structure of Ree groups
• Solvability of groups of odd order
• The characterization of finite groups with abelian Sylow 2-subgroups
• Theorems Like Sylow's
• Conjugacy of Odd order Hall Subgroups
• On a Conjecture of Philip Hall
• Hall subgroups of the symmetric groups

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