Groups with the weak minimal condition for non-subnormal subgroups

DOI10.1007/BF01783473zbMath0939.20040OpenAlexW3085801718MaRDI QIDQ1817933

Howard Smith, Leonid A. Kurdachenko

Publication date: 4 January 2000

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/bf01783473

zbMATH Keywords

subnormal subgroupsgeneralized radical groupssoluble-by-finite minimax groupsdescending \(\infty\)-chainsweak minimal condition on non-subnormal subgroups

Mathematics Subject Classification ID

Generalizations of solvable and nilpotent groups (20F19) Other classes of groups defined by subgroup chains (20F22) Chains and lattices of subgroups, subnormal subgroups (20E15)

Related Items (7)

On conormal subgroups ⋮ Groups satisfying weak chain conditions on non-modular subgroups ⋮ Groups with the weak maximal condition on non-permutable subgroups ⋮ A real chain condition for groups ⋮ Unnamed Item ⋮ Groups with all subgroups either subnormal or self-normalizing. ⋮ Groups with small deviation for non-subnormal subgroups.

Cites Work

• Properties of groups inherited by normal subgroups
• Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal)
• Groups satisfying weak minimum and maximum conditions for subnormal subgroups
• fc-groups in which the orders of the elements of the periodic part are bounded
• Groups with weak minimality and maximality conditions for subgroups which are not normal
• Groups with subnormality for all subgroups that are not finitely generated
• Some properties of groups inherited by normal subgroups of finite index
• Theory of minimax groups
• Summands of Separable Abelian Groups: Dedicated to Paul Turán on his 60th Birthday
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