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- Title
Partially commutative metabelian groups: centralizers and elementary equivalence.
- Authors
Gupta, Ch.; Timoshenko, E.
- 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.
- Subjects
NILPOTENT groups; COMMUTATORS (Operator theory); FINITE groups; LINEAR operators; OPERATOR theory
- Publication
Algebra & Logic, 2009, Vol 48, Issue 3, p173
- ISSN
0002-5232
- Publication type
Article
- DOI
10.1007/s10469-009-9051-3