Virtually free finite-normal-subgroup-free groups are strongly verbally closed

DOI10.1016/j.jalgebra.2018.05.028zbMath1401.20048arXiv1712.03406OpenAlexW2771670590WikidataQ129726764 ScholiaQ129726764MaRDI QIDQ724281

Veronika Yu. Miroshnichenko, Anton A. Klyachko, Andrey M. Mazhuga

Publication date: 25 July 2018

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

Full work available at URL: https://arxiv.org/abs/1712.03406

zbMATH Keywords

algebraically closed subgroupsretracts of groupsverbally 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 (5)

Finite and nilpotent strongly verbally closed groups ⋮ Verbally closed subgroups of free solvable groups ⋮ 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

• Unnamed Item
• On certain \(C\)-test words for free groups
• Strongly verbally closed 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

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