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Properties and universal theories for partially commutative nilpotent metabelian groups

Algebra and Logic Aims and scope

Partially commutative nilpotent metabelian groups are considered. We describe how annihilators of elements of the commutator subgroup of a group G, as well as centralizers of elements of G in its commutator subgroup G′, are structured. It turns out that in the case where a defining graph of a group is a tree, the intersection of centralizers of distinct vertices and G′ coincides with the last nontrivial commutator subgroup of G. Universal theories for partially commutative nilpotent metabelian groups are compared: conditions on defining graphs of two partially commutative nilpotent metabelian groups are formulated which are sufficient for the two groups to have equal universal theories; conditions on defining graphs of two partially commutative metabelian groups are specified which are sufficient for the two groups to be universally equivalent; a criterion is given that decides whether two partially commutative nilpotent metabelian groups defined by trees are universally equivalent.

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Correspondence to E. I. Timoshenko.

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Translated from Algebra i Logika, Vol. 51, No. 4, pp. 429-457, July-August, 2012.

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Gupta, C.K., Timoshenko, E.I. Properties and universal theories for partially commutative nilpotent metabelian groups. Algebra Logic 51, 285–305 (2012). https://doi.org/10.1007/s10469-012-9192-7

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  • DOI: https://doi.org/10.1007/s10469-012-9192-7

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