Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups

DOI10.1134/S0037446617030168zbMath1400.20026OpenAlexW2648472642MaRDI QIDQ2400744

Assem Adilbekkizi Konyrkhanova, N. G. Khisamiev, Vitaliĭ Roman'kov

Publication date: 30 August 2017

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446617030168

zbMATH Keywords

nilpotent groupretractalgebraically (verbally) closed subgroupgroup of integer unitriangular matrices

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Nilpotent groups (20F18) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Algebraic geometry over groups; equations over groups (20F70)

Related Items (3)

Finite and nilpotent strongly verbally closed groups ⋮ Solvability of equations in classes of solvable groups and Lie algebras ⋮ Equations in acylindrically hyperbolic groups and verbal closedness

Cites Work

• Diophantine questions in the class of finitely generated nilpotent groups
• Model-theoretic and algorithmic questions in group theory
• Combinatorial group theory.
• Verbally and existentially closed subgroups of free nilpotent groups.
• Existentially closed subgroups of free nilpotent groups.
• Equations over groups
• Verbally closed subgroups of free groups
• Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups
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