Pronormality and submaximal \(\mathfrak{X}\)-subgroups on finite groups

DOI10.1007/S40304-018-0154-9zbMath1502.20014OpenAlexW3007017092MaRDI QIDQ1757188

Wen-Bin Guo, Danila Olegovitch Revin

Publication date: 2 January 2019

Published in: Communications in Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40304-018-0154-9

zbMATH Keywords

pronormal subgroupsubmaximal \(\mathfrak{X}\)-subgroupHall \(\pi\)-subgroupsubgroup of odd index

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) Maximal subgroups (20E28) Finite simple groups and their classification (20D05) Subnormal subgroups of abstract finite groups (20D35) Products of subgroups of abstract finite groups (20D40)

Related Items (15)

On the pronormality of subgroups of odd index in some direct products of finite groups ⋮ The reduction theorem for relatively maximal subgroups ⋮ Submaximal soluble subgroups of odd index in alternating groups ⋮ On embedding theorems for \({\mathfrak{X}}\)-subgroups ⋮ Equivalence of the existence of nonconjugate and nonisomorphic Hall \(\pi\)-subgroups ⋮ On the heritability of the Sylow -theorem by subgroups ⋮ Examples of nonpronormal relatively maximal subgroups of finite simple groups ⋮ Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal ⋮ Maximal solvable subgroups of odd index in symmetric groups ⋮ Automorphisms of nonsplit extensions of \(2\)-groups by \(\mathrm{PSL}_2(q)\) ⋮ On the behavior of π-submaximal subgroups under homomorphisms ⋮ The Wielandt-Hartley theorem for submaximal \(\mathfrak{X}\)-subgroups ⋮ Submaximal and epimaximal \(\mathfrak{X}\)-subgroups ⋮ On \(\pi \)-submaximal subgroups of minimal nonsolvable groups ⋮ Relatively maximal subgroups of odd index in symmetric groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the pronormality of subgroups of odd index in finite simple groups.
• On the pronormality of Hall subgroups.
• On the class of groups with pronormal Hall \(\pi\)-subgroups.
• On the heritability of the property \(D_\pi\) by subgroups.
• Classification of maximal subgroups of odd index in finite groups with alternating socle.
• The existence of pronormal \(\pi\)-Hall subgroups in \(E_\pi\)-groups.
• Arithmetic of conjugacy of \(p\)-complements.
• A conjugacy criterion for Hall subgroups in finite groups.
• On the number of classes of conjugate Hall subgroups in finite simple groups.
• Frattini argument for Hall subgroups.
• Classification of maximal subgroups of odd index in finite simple classical groups.
• Pronormal regular subgroups of a finite symmetric group
• On \(p\)-complements of finite groups.
• Primitive permutation groups of odd degree, and an application to finite projective planes
• New criteria for the solvability of finite groups
• Finite soluble groups
• On the pronormality of subgroups of odd index in some extensions of finite groups
• Pronormality of Hall subgroups in their normal closure
• Classification and properties of the \(\pi \)-submaximal subgroups in minimal nonsolvable groups
• Classification of maximal subgroups of odd index in finite simple classical groups: addendum
• Pronormality of Hall subgroups in finite simple groups.
• Maximal and submaximal \(\mathfrak{X}\)-subgroups
• Isomorphism problem for relational structures with a cyclic automorphism
• 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.
• On pronormality and strong pronormality of Hall subgroups
• A pronormality criterion for supplements to abelian normal subgroups
• Abnormality criteria for \(p\)-complements
• On the pronormality of subgroups of odd index in finite simple symplectic groups
• Normalizers of the Sylow 2-subgroups in finite simple groups.
• Zum Satz von Sylow. II
• A theorem of Sylow type for finite groups
• Maximal \(\pi\)-subgroups of the symmetric groups
• Groups generated by a class of elements of order 3
• Pronormality of Hall subgroups in almost simple groups.
• Unsolved Problems in Group Theory. The Kourovka Notebook
• Structure Theory for Canonical Classes of Finite Groups
• An existence criterion for Hall subgroups of finite groups
• Theorems of Sylow type
• Theorems Like Sylow's
• Carter subgroups of finite almost simple groups
• The {ie210-01}-property in finite simple groups
• The Primitive Permutation Groups of Odd Degree
• On regular pronormal subgroups of symmetric groups
• RELATIONS ADMITTING A TRANSITIVE GROUP OF AUTOMORPHISMS
• Isomorphism problem for a class of point-symmetric structures
• Conjugacy of Odd order Hall Subgroups
• Nonsolvable finite groups all of whose local subgroups are solvable
• An Analog for the Frattini Factorization of Finite Groups
• A Characteristic Property of Soluble Groups

This page was built for publication: Pronormality and submaximal \(\mathfrak{X}\)-subgroups on finite groups