DSpace Arşivi :: by Yazar "Belegradek, Oleg" değerine göre listeleniyor

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Homogeneity in relatively free groups
(Springer Heidelberg, 2012) Belegradek, Oleg
We prove that any torsion-free, residually finite relatively free group of infinite rank is not -homogeneous. This generalizes Sklinos' result that a free group of infinite rank is not -homogeneous, and, in particular, gives a new simple proof of that result.
Local embeddability
(Luhansk Taras Shevchenko Natl Univ, 2012) Belegradek, Oleg
For an arbitrary class of algebraic structures we consider a notion of a structure locally embeddable to structures of the class. This generalizes the notion of a group locally embeddable to finite groups studied by Vershik and Gordon. We give various model-theoretic characterizations of such structures. Some of them generalize known group-theoretic results.
The model theory of the field of reals with a subgroup of the unit circle
(Wiley, 2008) Belegradek, Oleg; Zilber, Boris
We describe definable sets in the field of reals augmented by a predicate for a finite rank multiplicative group Gamma of complex numbers contained in the unit circle . This structure interprets the quotient-space /Gamma which, for Gamma infinite cyclic, is related to the quantum torus. Every definable set is proved to be a Boolean combination of existentially definable sets. We give a complete set of axioms for the theory of such a structure.