Geodesic
Group signature formulas constructed from graphs
Algebra i logika, Tome 61 (2022) no. 2, pp. 201-219.

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Given a finite undirected graph $\Gamma$ without loops, we define a sentence $\Phi(\Gamma)$ of group theory. A sequence of graphs $\Gamma_i$ is used to obtain a sequence of sentences $\Phi(\Gamma_i)$. These are employed to determine the $\Gamma$-dimension of a group and to study properties of the dimension. Under certain restrictions on a group, the known centralizer dimension is the $\Gamma$-dimension for some sequence of graphs. We mostly focus on dimensions defined by using linear graphs and cycles. Dimensions for a number of partially commutative metabelian groups are computed.
Keywords: undirected graph, partially commutative metabelian group.
Mots-clés : $\Gamma$-dimension of group 
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E. I. Timoshenko. Group signature formulas constructed from graphs. Algebra i logika, Tome 61 (2022) no. 2, pp. 201-219. http://geodesic.mathdoc.fr/item/AL_2022_61_2_a3/

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