Modules over nilpotent groups of finite rank

DOI10.1007/BF01978845zbMath0604.20037OpenAlexW1965111613MaRDI QIDQ1083543

A. V. Tushev, D. I. Zajtsev, Leonid A. Kurdachenko

Publication date: 1985

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01978845

zbMATH Keywords

metabelian groupscentral seriesmetanilpotent groupsmodules over group ringsminimal condition for normal subgroupsminimality conditions on infinite soluble groupsnilpotent group of finite free rankperiodic soluble groupsweak minimality conditions

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Other classes of groups defined by subgroup chains (20F22) Nilpotent groups (20F18) Chains and lattices of subgroups, subnormal subgroups (20E15) Derived series, central series, and generalizations for groups (20F14) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Related Items

Locally soluble-by-finite groups with the weak minimal condition on non-nilpotent subgroups ⋮ On conormal subgroups ⋮ Groups with a maximality condition for some non-normal subgroups ⋮ Groups whose proper quotients have finite derived subgroups ⋮ On groups with many almost normal subgroups ⋮ Anti-CC-groups and anti-PC-groups. ⋮ Just non-Artinian modules over some group rings ⋮ Periodic Linear Groups with the Weak Chain Conditions on Subgroups of Infinite Central Dimension

Cites Work

• Soluble groups which are products of nilpotent minmax groups
• On the Finiteness of Certain Soluble Groups
• Uncountable Artinian Modules and Uncountable Soluble Groups Satisfying Min-n
• Finiteness Conditions for Soluble Groups
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