Verbally and existentially closed subgroups of free nilpotent groups.

DOI10.1007/s10469-013-9245-6zbMath1330.20049OpenAlexW2063093897MaRDI QIDQ2342102

N. G. Khisamiev, Vitaliĭ Roman'kov

Publication date: 8 May 2015

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-013-9245-6

zbMATH Keywords

varieties of nilpotent groupsfree nilpotent groupsretractsalgebraically closed subgroupsverbally closed subgroupsexistentially closed subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Nilpotent groups (20F18) Quasivarieties and varieties of groups (20E10) Algebraic geometry over groups; equations over groups (20F70)

Related Items (12)

Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups ⋮ On free decompositions of verbally closed subgroups in free products of finite groups ⋮ Strongly verbally closed groups ⋮ Verbally closed virtually free subgroups ⋮ 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 ⋮ Retracts and verbally closed subgroups with respect to relatively free soluble groups ⋮ Free products of groups are strongly verbally closed ⋮ The Klein bottle group is not strongly verbally closed, though awfully close to being so ⋮ Existentially closed subgroups of free nilpotent groups. ⋮ Equations in acylindrically hyperbolic groups and verbal closedness

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