Groups with few non-nilpotent subgroups

DOI10.1017/S0017089500032031zbMath0883.20018MaRDI QIDQ4352112

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Publication date: 22 March 1998

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

maximal subgroupssubnormal subgroupslocally nilpotent groupsnon-nilpotent subgroups

Mathematics Subject Classification ID

Maximal subgroups (20E28) Generalizations of solvable and nilpotent groups (20F19) Chains and lattices of subgroups, subnormal subgroups (20E15) Finite nilpotent groups, (p)-groups (20D15) Local properties of groups (20E25)

Related Items (17)

Locally soluble-by-finite groups with the weak minimal condition on non-nilpotent subgroups ⋮ Locally (soluble-by-finite) groups with all proper insoluble subgroups of finite rank ⋮ On minimal non-(residually nilpotent) locally graded groups ⋮ On minimal non-(torsion-by-nilpotent) and non-((locally finite)-by-nilpotent) groups ⋮ Infinite minimal non-hypercyclic groups ⋮ Groups with some restrictions on non-Baer subgroups ⋮ Groups with finitely many isomorphic classes of relevant subgroups ⋮ Groups whose proper subgroups are locally finite-by-nilpotent. ⋮ Linear groups whose proper subgroups are close to being nilpotent ⋮ GROUPS WITH ALL PROPER SUBGROUPS (FINITE RANK)-BY-NILPOTENT. II ⋮ Retracted article: Barely transitivity and hypercentrality in locally finite \(p\)-groups. ⋮ A survey on just-non-\(\mathfrak X\) groups. ⋮ ON GROUPS WHOSE PROPER SUBGROUPS ARE CHERNIKOV-BY-BAER OR (PERIODIC DIVISIBLE ABELIAN)-BY-BAER ⋮ Soluble minimal non-(finite-by-Baer)-groups. ⋮ On Minimal Non-Baer-Groups ⋮ Groups with small deviation for non-subnormal subgroups. ⋮ Groups with many \(FC\)-subgroups

Cites Work

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• Torsionsfreie Gruppen, deren Untergruppen alle subnormal sind. (Torsion free groups all of whose subgroups are subnormal)
• Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal)
• Groups of Heineken-Mohamed
• Groups with weak minimality and maximality conditions for subgroups which are not normal
• A group with trivial centre satisfying the normalizer condition
• Some properties of groups inherited by normal subgroups of finite index
• Soluble products of nilpotent groups
• Groups with many nilpotent subgroups

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