Verbally closed virtually free subgroups

DOI10.1070/SM8942zbMath1452.20041arXiv1702.07761OpenAlexW2592989798MaRDI QIDQ4581454

Anton A. Klyachko, Andrey M. Mazhuga

Publication date: 20 August 2018

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.07761

zbMATH Keywords

retractsalgebraically closed subgroupsverbally closed subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Algebraic geometry over groups; equations over groups (20F70)

Related Items (8)

Strongly verbally closed groups ⋮ Finite and nilpotent strongly verbally closed groups ⋮ Verbally closed subgroups of free solvable groups ⋮ Retracts and verbally closed subgroups with respect to relatively free soluble groups ⋮ Free products of groups are strongly verbally closed ⋮ Virtual retraction and Howson’s theorem in pro-$p$ groups ⋮ The Klein bottle group is not strongly verbally closed, though awfully close to being so ⋮ Equations in acylindrically hyperbolic groups and verbal closedness

Cites Work

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• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• On certain \(C\)-test words for free groups
• Two theorems about equationally Noetherian groups
• Verbally and existentially closed subgroups of free nilpotent groups.
• On free decompositions of verbally closed subgroups in free products of finite groups
• Equations over groups
• Verbally closed subgroups of free groups
• Finite and infinite cyclic extensions of free groups
• The residual finiteness of positive one-relator groups

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