On the number of normal subgroups of an uncountable soluble group

DOI10.1007/BF01246116zbMath0528.20001OpenAlexW2070620591MaRDI QIDQ786906

James Wiegold, Frank Okoh, Howard Smith, Robert G. Burns

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1007/bf01246116

zbMATH Keywords

metabelian groupsnumber of normal subgroupsnumber of submodulesuncountable abelian-by-polycyclic groupuncountable cardinality

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Subgroup theorems; subgroup growth (20E07) Solvable groups, supersolvable groups (20F16) Commutative Noetherian rings and modules (13E05) Chains and lattices of subgroups, subnormal subgroups (20E15)

Related Items (7)

On modules \(M\) for which \(N\cong M\) for every submodule \(N\) of size \(|M|\) ⋮ GROUPS IN WHICH ALL LARGE SUBGROUPS HAVE BOUNDED NEAR DEFECT ⋮ Groups with countably many subgroups. ⋮ Jonsson and HS modules over commutative rings ⋮ Jónsson Modules over Noetherian Rings ⋮ On infinite modules \(M\) over a Dedekind domain for which \(N\cong M\) for every submodule \(N\) of cardinality \(|M|\) ⋮ Counting submodules of a module over a Noetherian commutative ring

Cites Work

• On the Number of Normal Subgroups of an Infinite Group
• Uncountable Artinian Modules and Uncountable Soluble Groups Satisfying Min-n
• Decomposing Euclidean space with a small number of smooth sets

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