Geodesic
Equations in acylindrically hyperbolic groups and verbal closedness
Oleg Bogopolski1
1University of Szczecin, Poland; Heinrich-Heine-Universität Düsseldorf, Germany
Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 613-682

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DOI

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 an equation has the form w(x1​,...,xn​)=h, where w∈F(X), h∈H).
DOI : 10.4171/ggd/661
Classification : 20-XX
Mots-clés : equations over a group, acylindrically hyperbolic group, algebraically closed subgroup, verbally closed subgroup, retract, relatively hyperbolic group, equationally Noetherian group

Oleg Bogopolski  1

1 University of Szczecin, Poland; Heinrich-Heine-Universität Düsseldorf, Germany 
Oleg Bogopolski. Equations in acylindrically hyperbolic groups and verbal closedness. Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 613-682. doi: 10.4171/ggd/661
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     year = {2022},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/661/}
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