Equivalence of the existence of nonconjugate and nonisomorphic Hall \(\pi\)-subgroups

DOI10.1134/S0081543818090109zbMath1499.20051OpenAlexW2920871156MaRDI QIDQ2424183

Danila Olegovitch Revin, Aleksandr Aleksandrovich Buturlakin, Wen-Bin Guo

Publication date: 24 June 2019

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543818090109

zbMATH Keywords

conjugate subgroupsHall \(\pi\)-subgroup\(\mathcal{C}_\pi\) condition

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Products of subgroups of abstract finite groups (20D40)

Cites Work

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• On the pronormality of Hall subgroups.
• On the class of groups with pronormal Hall \(\pi\)-subgroups.
• The existence of pronormal \(\pi\)-Hall subgroups in \(E_\pi\)-groups.
• Arithmetic of conjugacy of \(p\)-complements.
• Frattini argument for Hall subgroups.
• On \(p\)-complements of finite groups.
• Pronormality of Hall subgroups in their normal closure
• Pronormality and submaximal \(\mathfrak{X}\)-subgroups on finite groups
• Pronormality of Hall subgroups in finite simple groups.
• On pronormality and strong pronormality of Hall subgroups
• Structure Theory for Canonical Classes of Finite Groups
• Theorems of Sylow type
• Theorems Like Sylow's
• Conjugacy of Odd order Hall Subgroups

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