Criteria for permutability to be transitive in finite groups

DOI10.1006/jabr.1998.7964zbMath0948.20015OpenAlexW2031997636MaRDI QIDQ1969361

Ben Brewster, James C. Beidleman, Derek J. S. Robinson

Publication date: 8 May 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7964

zbMATH Keywords

products of subgroupspermutable subgroupsmodular Sylow subgroups\(T\)-groupssoluble \(PT\)-groups

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Series and lattices of subgroups (20D30) Modular lattices, Desarguesian lattices (06C05) Products of subgroups of abstract finite groups (20D40)

Related Items (33)

Local characterizations of infinite groups whose ascendant subgroups are permutable ⋮ Finite groups in which permutability is a transitive relation on their Frattini factor groups. ⋮ On periodic radical groups in which permutability is a transitive relation. ⋮ Some new characterizations of PST-groups. ⋮ Finite groups with transitive semipermutability ⋮ Unnamed Item ⋮ Finite groups in which \(\tau\)-quasinormality is a transitive relation. ⋮ Periodic linear groups in which permutability is a transitive relation ⋮ On hypercentral factor groups from certain classes ⋮ Unnamed Item ⋮ Algorithms for permutability in finite groups. ⋮ The intersection map of subgroups and certain classes of finite groups. ⋮ Some classes of finite groups and mutually permutable products. ⋮ Note on finite groups in which \(c\)-permutability is transitive. ⋮ The structure of finite groups in which permutability is a transitive relation ⋮ G-covering subgroup systems for the classes of finite soluble PST-groups ⋮ Extensions with overlap. ⋮ Generalizations of Groups in which Normality Is Transitive ⋮ Finite soluble groups with permutable subnormal subgroups ⋮ Sylow permutable subnormal subgroups of finite groups II ⋮ Pairwise -connected Products of Certain Classes of Finite Groups ⋮ On a Class of p-Soluble Groups ⋮ Infinite groups with many permutable subgroups. ⋮ A Local Approach to Certain Classes of Finite Groups ⋮ \(G\)-covering subgroup systems for some classes of \(\sigma\)-soluble groups ⋮ Solvable PST-groups, strong Sylow bases and mutually permutable products. ⋮ Finite groups with subgroups supersoluble or subnormal. ⋮ On some arithmetic properties of nite groups ⋮ On self-normalizing subgroups of finite groups ⋮ Minimality and locally defined classes of groups. ⋮ A note on finite 𝒫𝒮𝒯-groups ⋮ Sylow permutable subnormal subgroups of finite groups ⋮ On \(\sigma\)-subnormal and \(\sigma\)-permutable subgroups of finite groups.

Cites Work

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• Zur Sylowstruktur auflösbarer Gruppen
• Subgroup lattices of groups
• The embedding of quasinormal subgroups in finite groups
• Gruppen, in denen das Normalteilersein transitiv ist.
• A Note on Finite Groups in Which Normality is Transitive
• Finite Groups with Pro-Normal Subgroups

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