Properties and universal theories for partially commutative nilpotent metabelian groups
 Ch. K. Gupta,
 E. I. Timoshenko
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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.
 Ch. K. Gupta and E. I. Timoshenko, “Partially commutative metabelian groups: Centralizers and elementary equivalence,” Algebra Logika, 48, No. 3, 309–341 (2009). CrossRef
 E. I. Timoshenko, “Universal equivalence of partially commutative metabelian groups,” Algebra Logika, 49, No. 2, 263–289 (2010). CrossRef
 Ch. K. Gupta and E. I. Timoshenko, “Universal theories for partially commutative metabelian groups,” Algebra Logika, 50, No. 1, 3–25 (2011).
 E. I. Timoshenko, “A Mal’tsev basis for a partially commutative nilpotent metabelian group,” Algebra Logika, 50, No. 5, 647–658 (2011). CrossRef
 V. A. Roman’kov, “Generators for the automorphism groups of free metabelian propgroups,” Sib. Mat. Zh., 33, No. 5, 878–890 (1992). CrossRef
 A. A. Mishchenko and A. V. Treier, “Structure of centralizers for a partially commutative nilpotent Qgroup of class two,” Vestnik Omsk Gos. Univ. (2007), pp. 98–102.
 A. A. Mishchenko, “Universal equivalence of partially commutative class two nilpotent $ \mathbb{Q} $ groups,” Vestnik Omsk Univ. (2008), pp. 61–67.
 V. A. Roman’kov, “Width of verbal subgroups of solvable groups,” Algebra Logika, 21, No. 1, 60–72 (1982).
 A. A. Mishchenko and E. I. Timoshenko, “Universal equivalence of partially commutative nilpotent groups,” Sib. Mat. Zh., 52, No. 5, 1113–1122 (2011). CrossRef
 Title
 Properties and universal theories for partially commutative nilpotent metabelian groups
 Journal

Algebra and Logic
Volume 51, Issue 4 , pp 285305
 Cover Date
 20120901
 DOI
 10.1007/s1046901291927
 Print ISSN
 00025232
 Online ISSN
 15738302
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 partially commutative nilpotent metabelian groups
 annihilator
 centralizer
 graph of group
 tree
 universal theory
 Industry Sectors
 Authors

 Ch. K. Gupta ^{(1)}
 E. I. Timoshenko ^{(2)}
 Author Affiliations

 1. University of Manitoba, Winnipeg, R3T 2N2, Canada
 2. Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630092, Russia