Given a finite undirected graph Γ without loops, we define a sentence Φ(Γ) of group theory. A sequence of graphs Γi is used to obtain a sequence of sentences Φ(Γi). These are employed to determine the Γ-dimension of a group and to study properties of the dimension. Under certain restrictions on a group, the known centralizer dimension is the Γ-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.
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Translated from Algebra i Logika, Vol. 61, No. 2, pp. 201-219, March-April, 2022. Russian DOI: https://doi.org/10.33048/alglog.2022.61.204
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Timoshenko, E.I. Group Signature Formulas Constructed from Graphs. Algebra Logic 61, 139–152 (2022). https://doi.org/10.1007/s10469-022-09682-y
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DOI: https://doi.org/10.1007/s10469-022-09682-y