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math.GR2025
Equationally separable classes of groups
Alexander Buturlakin, Anton Klyachko, Denis Osin
Over each nontrivial finite group , there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing $G…
math.GR2024
Finite symmetric groups are strongly verbally closed
Olga K. Karimova, Anton A. Klyachko
Answering a question of A. V. Vasil'ev, we show that each finite symmetric (or alternating) group is a retract of any group containing as a verbally closed subgroup.
math.GR2024
The centre of a finitely generated strongly verbally closed group is almost always pure
Filipp D. Denissov, Anton A. Klyachko
The assertion in the title implies that many interesting groups (e.g., all non-abelian braid groups or ) are not strongly verbally closed, i.e., they emb…