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- W2922833114 abstract "Let $H$ be an acylindrically hyperbolic group without nontrivial finite normal subgroups. We show that any finite system $S$ of equations with constants from $H$ is equivalent to a single equation. We also show that the algebraic set associated with $S$ is, up to conjugacy, a projection of the algebraic set associated with a single splitted equation (such equation has the form $w(x_1,dots,x_n)=h$, where $win F(X)$, $hin H$). From this we deduce the following statement: Let $G$ be an arbitrary overgroup of the above group $H$. Then $H$ is verbally closed in $G$ if and only if it is algebraically closed in $G$. Another corollary: If $H$ is a non-cyclic torsion-free hyperbolic group, then every (possibly infinite) system of equations with finitely many variables and with constants from $H$ is equivalent to a single equation." @default.
- W2922833114 created "2019-04-01" @default.
- W2922833114 creator A5064620696 @default.
- W2922833114 date "2019-03-24" @default.
- W2922833114 modified "2023-09-27" @default.
- W2922833114 title "On finite systems of equations in acylindrically hyperbolic groups." @default.
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