Finite groups with non-nilpotent maximal subgroups.

DOI10.1007/S00605-012-0432-7zbMath1277.20017OpenAlexW1986365321MaRDI QIDQ368516

Xianggui Zhong, Jiakuan Lu, Linna Pang

Publication date: 23 September 2013

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-012-0432-7

zbMATH Keywords

finite groupsmaximal subgroupssolvable groups\(p\)-nilpotent groupsminimal non-nilpotent groupsQTI-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) Maximal subgroups (20E28) Special subgroups (Frattini, Fitting, etc.) (20D25)

Related Items (10)

Some generalizations of Shao and Beltrán’s theorem ⋮ Sylow towers in groups where the index of every non-nilpotent maximal subgroup is prime ⋮ Finite groups in which every maximal subgroup is nilpotent or normal or has p′-order ⋮ Indices of maximal invariant subgroups and solvability of finite groups ⋮ On finite groups in which some particular maximal invariant subgroups have indices a prime-power ⋮ On finite groups with non-nilpotent subgroups. ⋮ Finite groups in which every non-nilpotent subgroup is a TI-subgroup or has \(p'\)-order ⋮ On TI-subgroups and QTI-subgroups of finite groups ⋮ Restrictions on maximal invariant subgroups implying solvability of finite groups ⋮ Orbits of maximal invariant subgroups and solvability of finite groups

Cites Work

• Unnamed Item
• Unnamed Item
• A note on TI-subgroups of finite groups.
• Finite groups whose Abelian subgroups are TI-subgroups.
• Finite groups all of whose Abelian subgroups are QTI-subgroups.
• On finite insoluble groups with nilpotent maximal subgroups
• Some results on \(p\)-nilpotence and solubility of finite groups
• Finite \(p\)-groups whose Abelian subgroups have a trivial intersection.
• Classification of Finite Groups with a CC-Subgroup
• Finite Groups all of Whose Second Maximal Subgroups are QTI-Subgroups
• Endliche Gruppen I
• On a class of doubly transitive groups

This page was built for publication: Finite groups with non-nilpotent maximal subgroups.