On the number of classes of conjugate Hall subgroups in finite simple groups.

DOI10.1016/J.JALGEBRA.2010.09.014zbMath1219.20020arXiv0912.1922OpenAlexW2022728291MaRDI QIDQ627987

Danila Olegovitch Revin, Evgeny P. Vdovin

Publication date: 4 March 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1922

zbMATH Keywords

Hall subgroupsnumbers of conjugacy classesclassical groupsfinite groups of Lie typesubgroups of odd index

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (27)

On finite groups factorized by σ-nilpotent subgroups ⋮ The reduction theorem for relatively maximal subgroups ⋮ Classification and properties of the \(\pi \)-submaximal subgroups in minimal nonsolvable groups ⋮ On the pronormality of Hall subgroups. ⋮ A conjugacy criterion for Hall subgroups in finite groups. ⋮ On the class of groups with pronormal Hall \(\pi\)-subgroups. ⋮ Nonabelian composition factors of a finite group whose all maximal subgroups are Hall. ⋮ On the heritability of the Sylow -theorem by subgroups ⋮ Designs from maximal subgroups and conjugacy classes of Ree groups ⋮ On the heritability of the property \(D_\pi\) by subgroups. ⋮ On intersections of solvable Hall subgroups in finite simple exceptional groups of Lie type. ⋮ The existence of pronormal \(\pi\)-Hall subgroups in \(E_\pi\)-groups. ⋮ On ℱ-injectors of fitting set of a finite group ⋮ Nonabelian composition factors of a finite group whose maximal subgroups of odd indices are Hall subgroups ⋮ Pronormality and submaximal \(\mathfrak{X}\)-subgroups on finite groups ⋮ Conjugacy of maximal and submaximal \(\mathfrak{X}\)-subgroups ⋮ Computing Hall subgroups of finite groups ⋮ Pronormality of Hall subgroups in finite simple groups. ⋮ On Baer-Suzuki \(\pi\)-theorems. ⋮ On the class of groups with pronormal hall π-subgroups ⋮ Maximal and submaximal \(\mathfrak{X}\)-subgroups ⋮ Frattini argument for Hall subgroups. ⋮ A criterion for the existence of a solvable π-Hall subgroup in a finite group ⋮ On quantitative structure of small Ree groups ⋮ Some symmetric designs invariant under the small Ree groups ⋮ Hartley sets and injectors of a finite group ⋮ On some aspects of the Kegel-Wielandt \(\sigma \)-conjecture

Uses Software

• GAP

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