Geodesic
Algorithmic decidability of the universal equivalence problem for partially commutative nilpotent groups
Algebra i logika, Tome 52 (2013) no. 2, pp. 219-235.

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Let $G_\Gamma$ be a partially commutative group corresponding to a finite simple graph $\Gamma$. Given a finite simple graph $T$, an existential graph formula $\phi(T)$ is constructed. We describe an algorithm that answers the question whether $\phi(T)$ is satisfied on $G_\Gamma$, for an arbitrary simple graph $T$. Using this algorithm, we show that the universal equivalence problem for partially commutative class two nilpotent groups is algorithmically decidable.
Keywords: partially commutative nilpotent group, universal theory, satisfiability, decidability.
Mots-clés : binomial ring 
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A. A. Mishchenko; A. V. Treier. Algorithmic decidability of the universal equivalence problem for partially commutative nilpotent groups. Algebra i logika, Tome 52 (2013) no. 2, pp. 219-235. http://geodesic.mathdoc.fr/item/AL_2013_52_2_a5/

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