Free products of groups are strongly verbally closed

DOI10.1070/SM9115OpenAlexW3103825296MaRDI QIDQ5207126

Andrey M. Mazhuga

Publication date: 7 January 2020

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

Full work available at URL: https://arxiv.org/abs/1803.10634

zbMATH Keywords

algebraically closed subgroupsretracts of groupsverbally closed subgroups

Mathematics Subject Classification ID

Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Groups acting on trees (20E08) Algebraic geometry over groups; equations over groups (20F70)

Related Items (3)

Finite and nilpotent strongly verbally closed 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

• Virtually free finite-normal-subgroup-free groups are strongly verbally closed
• On certain elements of 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
• Verbally closed virtually free subgroups
• Uniqueness Theorems for Periodic Functions
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