Strongly verbally closed groups

DOI10.1016/j.jalgebra.2017.09.021zbMath1388.20065arXiv1707.02464OpenAlexW2963362943MaRDI QIDQ1675071

Andrey M. Mazhuga

Publication date: 26 October 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.02464

zbMATH Keywords

algebraically closed subgroupsretracts of groupsverbally closed subgroups

Mathematics Subject Classification ID

Free nonabelian groups (20E05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Quasivarieties and varieties of groups (20E10) Algebraic geometry over groups; equations over groups (20F70)

Related Items (6)

Finite and nilpotent strongly verbally closed groups ⋮ Verbally closed subgroups of free solvable groups ⋮ Virtually free finite-normal-subgroup-free groups are strongly verbally closed ⋮ Free products of groups are strongly verbally closed ⋮ 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

• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• On certain \(C\)-test words for free 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
• Verbally closed virtually free subgroups
• The residual finiteness of positive one-relator groups
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