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17.104 (2010)

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Let $\Gamma$ be a finite non-oriented graph on the set of vertices $\{x_1, \dots, x_n\}$ and let
$$S_\Gamma = \langle x_1, \dots, x_n \mid x_i x_j = x_j x_i \iff (x_i, x_j) \in \Gamma; \mathfrak{A}^2 \rangle$$ be a presentation of a partially commutative metabelian group $S_\Gamma$ in the variety of all metabelian groups. Is the universal theory of the group $S_\Gamma$ decidable?

Contributor: V. N. Remeslennikov, E. I. Timoshenko

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