Groups with subnormality for all subgroups that are not finitely generated

DOI10.1007/BF01759354zbMath0848.20023OpenAlexW1992057154MaRDI QIDQ1913375

Hermann Heineken, Leonid A. Kurdachenko

Publication date: 27 October 1996

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01759354

zbMATH Keywords

subnormal subgroupslocally finite groupsChernikov groupsradical groupsnon-subnormal subgroupsradical \(db\)-groups

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Generalizations of solvable and nilpotent groups (20F19) Chains and lattices of subgroups, subnormal subgroups (20E15)

Related Items (21)

Groups with all subgroups either modular or soluble of finite rank ⋮ SOME CRITERIA FOR EXISTENCE OF SUPPLEMENTS TO NORMAL SUBGROUPS AND THEIR APPLICATIONS ⋮ On the influence of transitively normal subgroups on the structure of some infinite groups. ⋮ Groups with a maximality condition for some non-normal subgroups ⋮ On groups with many almost normal subgroups ⋮ On groups whose transitively normal subgroups are either normal or self-normalizing. ⋮ Large norms in group theory ⋮ Unnamed Item ⋮ Groups with the maximum condition on non-nilpotent subgroups ⋮ Groups satisfying the double chain condition on non-subnormal subgroups ⋮ Anti-CC-groups and anti-PC-groups. ⋮ Groups with Finitely Many Normalizers of Non-polycyclic Subgroups ⋮ Abnormal, Pronormal, Contranormal, and Carter Subgroups in Some Generalized Minimax Groups ⋮ Groups whose all subgroups are ascendant or self-normalizing. ⋮ Groups with all subgroups either subnormal or self-normalizing. ⋮ On groups whose factor-group modulo the hypercentre has finite section \(p\)-rank. ⋮ Locally nilpotent linear groups with restrictions on their subgroups of infinite central dimension. ⋮ Groups with the weak minimal condition for non-subnormal subgroups ⋮ On a generalization of Baer Theorem ⋮ On Influence of Contranormal Subgroups on the Structure of Infinite Groups ⋮ Groups with finitely many non-isomorphic factor-groups

Cites Work

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• Auflösbare Gruppen mit endlichem Exponenten, deren Untergruppen alle subnormal sind. II. (Soluble groups of finite exponent all subgroups of which are subnormal. II)
• Torsionsfreie Gruppen, deren Untergruppen alle subnormal sind. (Torsion free groups all of whose subgroups are subnormal)
• Properties of groups inherited by normal subgroups
• Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal)
• Nilpotent residuals of subnormal subgroups
• fc-groups in which the orders of the elements of the periodic part are bounded
• Infinite groups with normality conditions on infinite subgroups
• On groups in which every subgroup is subnormal
• A group with trivial centre satisfying the normalizer condition
• Splitting over nilpotent and hypercentral residuals
• A dual approach to Černikov modules
• Radical groups

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