This article is cited in 33 papers

Partially commutative metabelian groups: centralizers and elementary equivalence

Ch. K. Gupta^a, E. I. Timoshenko<sup>b

a</sup> Dep. Math., Univ. Manitoba, Winnipeg, CANADA
^b Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, RUSSIA

Abstract: For partially commutative metabelian groups, annihilators of elements of commutator subgroups are described; canonical representations of elements are defined; approximability by torsion-free nilpotent groups is proved; centralizers of elements are described. Also, it is proved that two partially commutative metabelian groups have equal elementary theories iff their defining graphs are isomorphic, and that every partially commutative metabelian group is embeddable in a metabelian group with decidable universal theory.

Keywords: metabelian group, centralizer, annihilator, elementary equivalence.

UDC: 512.5

Received: 07.04.2008

 English version: Algebra and Logic, 2009, 48:3, 173–192

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