Yazar "Belegradek, Oleg V." seçeneğine göre listele

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  • Küçük Resim Yok
    Öğe
    Endomorphisms of relatively hyperbolic groups
    (World Scientific Publ Co Pte Ltd, 2008) Belegradek, Igor; Szczepanski, Andrzej; Belegradek, Oleg V.
    We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. If G is a nonelementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out( G) is infinite, then G splits over a slender group. If H is a nonparabolic subgroup of a relatively hyperbolic group, and if any isometric H-action on an R-tree is trivial, then H is Hopfian. If G is a nonelementary relatively hyperbolic group whose peripheral subgroups are finitely generated, then G has a nonelementary relatively hyperbolic quotient that is Hopfian. Any finitely presented group is isomorphic to a finite index subgroup of Out( H) for some group H with Kazhdan property ( T). ( This sharpens a result of Ollivier-Wise).
  • Küçük Resim
    Öğe
    The space of minimal structures
    (2014-02) Belegradek, Oleg V.
    For a signature L with at least one constant symbol, an L-structure is called minimal if it has no proper substructures. Let SL be the set of isomorphism types of minimal L-structures. The elements of SL can be identified with ultrafilters of the Boolean algebra of quantifier-free L-sentences, and therefore one can define a Stone topology on SL. This topology on SL generalizes the topology of the space of n-marked groups. We introduce a natural ultrametric on SL, and show that the Stone topology on SL coincides with the topology of the ultrametric space SL iff the ultrametric space SL is compact iff L is locally finite (that is, L contains finitely many n-ary symbols for any n