The influence of minimal subgroups on the structure of a finite group

DOI10.1090/S0002-9939-02-06547-4zbMath1028.20015OpenAlexW1675765252MaRDI QIDQ4779835

Yang Ming Li, Yan Ming Wang

Publication date: 28 October 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06547-4

zbMATH Keywords

finite groupsSylow subgroupsminimal subgroupssupersolvable groupsgeneralized Fitting subgroup\(\pi\)-quasinormal subgroupsmaximal normal quasinilpotent subgroups

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) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25)

Related Items (44)

On NearlyS-Permutable Subgroups of Finite Groups ⋮ \(\mathcal M^*\)-supplemented subgroups of finite groups. ⋮ Finite Groups withS-permutablen-maximal Subgroups ⋮ On 𝑐-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups ⋮ Finite groups with given \(s\)-embedded and \(n\)-embedded subgroups. ⋮ A characterization of the hypercyclically embedded subgroups of finite groups. ⋮ A generalized CAP-subgroup of a finite group. ⋮ On weakly \(\tau\)-quasinormal subgroups of finite groups. ⋮ Finite groups in which \(\tau\)-quasinormality is a transitive relation. ⋮ On s-semipermutable subgroups of finite groups. ⋮ On some primary subgroups and the structure of finite groups. ⋮ Onm-S-supplemented subgroups of finite groups ⋮ On \(\Pi\)-property and \(\Pi\)-normality of subgroups of finite groups. ⋮ Finite groups with \(S\)-quasinormally embedded or \(SS\)-quasinormal subgroups. ⋮ On Permutable Subgroups of Finite Groups II ⋮ \(\mathfrak Z\)-permutable subgroups and \(p\)-nilpotency of finite groups. II. ⋮ On Some Open Problems Related toX-Permutability of Subgroups ⋮ On \(ss\)-quasinormal or weakly \(s\)-permutably embedded subgroups of finite groups ⋮ A remark on \(\mathfrak Z\)-permutability of finite groups. ⋮ On weakly \(s\)-permutable subgroups of finite groups. ⋮ On weakly \(s\)-normal subgroups of finite groups. ⋮ On \(ss\)-quasinormal and weakly \(s\)-supplemented subgroups of finite groups. ⋮ Finite groups with \(S\)-supplemented \(p\)-subgroups. ⋮ On $$s$$ s -semipermutable or ss-quasinormal subgroups of finite groups ⋮ THE INFLUENCE OF MINIMAL SUBGROUPS ON THE STRUCTURE OF FINITE GROUPS ⋮ The influence of some primary subgroups on the structure of finite groups ⋮ On weakly \(s\)-semipermutable or \(ss\)-quasinormal subgroups of finite groups ⋮ A note on characterization of finite groups with some \(S\)-quasinormal subgroups. ⋮ On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups ⋮ \(\pi\)-quasinormally embedded and c-supplemented subgroup of finite group. ⋮ On the \(\mathcal X\Phi\)-hypercentre of finite groups. ⋮ A characteristic condition of finite nilpotent group ⋮ On Semi Cover-Avoiding Maximal Subgroups of Sylow Subgroups of Finite Groups ⋮ Finite groups with some weakly pronormal subgroups ⋮ Finite groups with NE-subgroups ⋮ On weakly \(S\)-embedded subgroups of finite groups. ⋮ Finite groups with S-quasinormal subgroups ⋮ The influence of s-conditionally permutable subgroups on finite groups. ⋮ On solubility and supersolubility of some classes of finite groups. ⋮ Semipermutable subgroups and \(s\)-semipermutable subgroups in finite groups ⋮ ON MINIMAL WEAKLY s-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS ⋮ Characterization of finite groups with some \(S\)-quasinormal subgroups. ⋮ Finite groups with some SB-subgroups ⋮ Some Conditions Under which a Finite Group Belongs to a Baer-Local Formation

Cites Work

• Sylow-Gruppen und Subnormalteiler endlicher Gruppen
• Finite solvable groups whose \(\mathfrak F\)-hypercenter contains all minimal subgroups
• Finite solvable groups whose \(\mathfrak F\)-hypercenter contains all minimal subgroups. II
• The influence of \(\pi\)-quasinormality of some subgroups on the structure of a finite group
• Finite groups whose minimal subgroups are normal
• Endliche Gruppen I
• The influence of minimal subgroups on the structure of finite groups
• The influence of minimal subgroups on the structure of finite groups

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