An existence criterion for Hall subgroups of finite groups

DOI10.1515/JGT.2010.037zbMath1227.20015arXiv0803.3868MaRDI QIDQ3083485

Danila Olegovitch Revin, Evgeny P. Vdovin

Publication date: 22 March 2011

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.3868

zbMATH Keywords

Hall subgroups\(E_\pi\)-groups

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20)

Related Items (16)

Abnormality criteria for \(p\)-complements ⋮ Classification and properties of the \(\pi \)-submaximal subgroups in minimal nonsolvable groups ⋮ On the pronormality of Hall subgroups. ⋮ Principal blocks for different primes. I ⋮ On the class of groups with pronormal Hall \(\pi\)-subgroups. ⋮ Nonabelian composition factors of a finite group whose all maximal subgroups are Hall. ⋮ Brauer's height zero conjecture for two primes holds true ⋮ The existence of pronormal \(\pi\)-Hall subgroups in \(E_\pi\)-groups. ⋮ Pronormality and submaximal \(\mathfrak{X}\)-subgroups on finite groups ⋮ On the class of groups with pronormal hall π-subgroups ⋮ Maximal and submaximal \(\mathfrak{X}\)-subgroups ⋮ Addendum to: ``Trivial intersection of blocks and nilpotent subgroups ⋮ Frattini argument for Hall subgroups. ⋮ A criterion for the existence of a solvable π-Hall subgroup in a finite group ⋮ Formations of finite $C_\pi $-groups ⋮ Groups of induced automorphisms and their application to studying the existence problem for Hall subgroups.

Cites Work

• On the existence of Hall subgroups
• Subdirect products of finite groups with Hall \(\pi\)-subgroups
• Theorems Like Sylow's
• Carter subgroups of finite almost simple groups
• The {ie210-01}-property in finite simple groups
• Conjugacy of Odd order Hall Subgroups

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