Finite normal subgroups of strongly verbally closed groups

DOI10.1515/JGTH-2023-0015zbMATH Open1548.20078MaRDI QIDQ6611933

Filipp D. Denissov

Publication date: 27 September 2024

Published in: Journal of Group Theory (Search for Journal in Brave)

zbMATH Keywords

equations over groupsalgebraically closed subgroupstrong retractstrong verbally closed group

Mathematics Subject Classification ID

Nilpotent groups (20F18) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Finite nilpotent groups, (p)-groups (20D15) Algebraic geometry over groups; equations over groups (20F70)

Cites Work

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• Virtually free finite-normal-subgroup-free groups are strongly verbally closed
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Strongly verbally closed groups
• Equations in acylindrically hyperbolic groups and verbal closedness
• Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups
• Verbally closed subgroups of free groups
• Verbally closed virtually free subgroups
• The Klein bottle group is not strongly verbally closed, though awfully close to being so
• Free products of groups are strongly verbally closed
• Finiteness Conditions for Soluble Groups
• Finite and nilpotent strongly verbally closed groups

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