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14.19 (1999)

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We say that a group $G$ has the Noetherian Equation Property if every system of equations over $G$ in finitely many variables is equivalent to some finite part of it. Does an arbitrary hyperbolic group have the Noetherian Equation Property?

Contributor: G. Baumslag, A. G. Myasnikov, V. N. Remeslennikov

Progress

Comment of 2013: the conjecture holds for torsion-free hyperbolic groups (Z. Sela, Proc. London Math. Soc., 99, no. 1 (2009), 217–273) and for the larger class of toral relatively hyperbolic groups (D. Groves, J. Geom. Topol., 9 (2005), 2319–2358).

Editors' comment: Yes, it does (R. Weidmann, C. Reinfeldt, Ann. Math. Blaise Pascal, 26, no. 2 (2019), 125–214).

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