A generalisation of Kramer's theorem and its applications

DOI10.1017/S0004972700020517zbMath1012.20010OpenAlexW1996241240MaRDI QIDQ3149463

Hua Quan Wei, Yang Ming Li, Yan Ming Wang

Publication date: 17 March 2003

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700020517

zbMATH Keywords

maximal subgroupsfinite soluble groupsSylow subgroupssaturated formationsminimal subgroupsFitting subgroupsupersoluble groups\(c\)-supplementation

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) Special subgroups (Frattini, Fitting, etc.) (20D25) Products of subgroups of abstract finite groups (20D40)

Related Items (42)

\(\mathcal M^*\)-supplemented subgroups of finite groups. ⋮ Finite groups with some maximal subgroups of Sylow subgroups \(\mathcal M\)-supplemented. ⋮ THE INFLUENCE OF Φ-S-SUPPLEMENTED SUBGROUPS ON THE STRUCTURE OF FINITE GROUPS ⋮ On 𝑐-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups ⋮ The finite groups with IC-property of subgroups ⋮ On weakly \(S\Phi\)-supplemented subgroups of finite groups ⋮ On \(\mathcal M\)-permutable Sylow subgroups of finite groups. ⋮ On weakly \(S\)-embedded and weakly \(\tau\)-embedded subgroups. ⋮ Weakly \(c\)-permutable subgroups of finite groups. ⋮ On \(c\)-supplemented subgroups of finite groups. ⋮ Finite Groups Whose Minimal Subgroups arec-Supplemented ⋮ Unnamed Item ⋮ \(c^\sharp\)-normality of groups and its properties. ⋮ On P_𝔉-Supplemented subgroups of finite groups ⋮ Onm-S-supplemented subgroups of finite groups ⋮ Finite groups with weakly \(s\)-semipermutable subgroups. ⋮ ON WEAKLY -SUPPLEMENTED SUBGROUPS OF SYLOW p-SUBGROUPS OF FINITE GROUPS ⋮ On generalized \(\mathfrak U\)-hypercentral subgroups of a finite group. ⋮ OnSQ-Supplemented Subgroups of Finite Groups ⋮ New criteria of supersolvability of finite groups ⋮ New Characterizations ofp-Supersolubility of Finite Groups ⋮ Finite groups with certain kind of subgroups weakly {\(c\)}-supplemented ⋮ Finite groups with given nearly SΦ-embedded subgroups ⋮ Finite groups with some primary subgroups \(ss\)-quasinormally embedded. ⋮ On one generalization of modular subgroups ⋮ \(Q\)-permutable subgroups of finite groups. ⋮ MAXIMAL SUBGROUPS OF A SYLOW p-SUBGROUP AND p-NILPOTENCY OF FINITE GROUPS ⋮ The c-Normal Embedding Property in Finite Groups (I) ⋮ SOME NEW CHARACTERISATIONS OF FINITE -SUPERSOLUBLE GROUPS ⋮ On nearly \(\mathcal M\)-supplemented subgroups of finite groups. ⋮ FINITE GROUPS WITH SOME 𝔉-SUPPLEMENTED SUBGROUPS ⋮ On ℳ-Permutable Maximal Subgroups of Sylow Subgroups of Finite Groups ⋮ On CAS-subgroups of finite groups. ⋮ On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups ⋮ On ℳ-supplemented subgroups of finite groups ⋮ Localc*-Supplementation of Some Subgroups in Finite Groups ⋮ On weakly ℨ-permutable subgroups of finite groups ⋮ Unnamed Item ⋮ The influence of \(\mathcal M\)-supplemented subgroups on the structure of finite groups. ⋮ On ℱ-Quasinormal Primary Subgroups of Finite Groups ⋮ Finite groups with given systems of \(m\)-\(S\)-complemented subgroups ⋮ On c*-normality and its properties

Cites Work

• Über Durchschnitte von Untergruppen endlicher auflösbarer Gruppen.
• \(C\)-normality of groups and its properties
• Finite groups whose minimal subgroups are normal
• ON c-NORMAL MAXIMAL AND MINIMAL SUBGROUPS OF SYLOW SUBGROUPS OF FINITE GROUPS
• The classification of (J, σ)-irreducible monoids of typeA₄
• C-Supplemented subgroups of finite groups
• Endliche Gruppen I
• On complemented subgroups of finite groups

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