On groups with all proper subgroups finite-by-abelian-by-finite

DOI10.1007/s00013-021-01580-6zbMath1483.20065OpenAlexW3130117981MaRDI QIDQ2031456

Fausto De Mari, Ulderico Dardano

Publication date: 9 June 2021

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-021-01580-6

zbMATH Keywords

CN-subgroupcommensurable subgroupcore-finite subgroupinfinite-rankminimal-non-\(\mathcal{P}\)

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Periodic groups; locally finite groups (20F50) Generalizations of solvable and nilpotent groups (20F19) Other classes of groups defined by subgroup chains (20F22) FC-groups and their generalizations (20F24)

Related Items (3)

ON GROUPS WHOSE SUBGROUPS ARE EITHER MODULAR OR CONTRANORMAL ⋮ Groups with many abelian or self-normalizing subgroups ⋮ On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup

Cites Work

• Large soluble groups and the control of embedding properties.
• Infinite locally finite groups of type PSL(2,K) or Sz(K) are not minimal under certain conditions
• Groups with the minimum condition on insoluble subgroups
• On groups with nilpotent by Černikov proper subgroups
• Groups with all proper subgroups nilpotent-by-finite rank
• Groups in which each subgroup is commensurable with a normal subgroup
• Theorem on groups of finite special rank
• A note on groups with nilpotent-by-finite proper subgroups
• Groups with all proper subgroups soluble-by-finite rank.
• Large and symmetric: the Khukhro-Makarenko theorem on laws -- without laws.
• A note on groups of infinite rank whose proper subgroups are abelian-by-finite
• Infinite minimal non-hypercyclic groups
• Locally Nilpotent p -Groups whose Proper Subgroups are Hypercentral or Nilpotent-by-Chernikov
• Groups with many modular or self-normalizing subgroups
• Inertial properties in groups
• A note on infinite groups whose subgroups are close to be normal-by-finite
• GROUPS WHOSE PROPER SUBGROUPS OF INFINITE RANK HAVE FINITE CONJUGACY CLASSES
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