A combinatorial proof of the extension property for partial isometries
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
A - finite actions and their automorphism groups.
Acyclic groups of automorphisms.
Amenable group actions on infinite graphs.
Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits
Autohomeomorphism groups of spaces with unique non-isolated point
Automorphism invariants for semigroups.
Automorphisms of models of bounded arithmetic
We establish the following model-theoretic characterization of the fragment IΔ₀ + Exp + BΣ₁ of Peano arithmetic in terms of fixed points of automorphisms of models of bounded arithmetic (the fragment IΔ₀ of Peano arithmetic with induction limited to Δ₀-formulae). Theorem A. The following two conditions are equivalent for a countable model of the language of arithmetic: (a) satisfies IΔ₀ + BΣ₁ + Exp; (b) for some nontrivial automorphism j of an end extension of that satisfies IΔ₀. Here is the...
Autormorphism groups of countable highly homogeneous partially ordererd sets.
Compactness conditions for semigroups of linear maps.
Conjugate homeomorphisms of the Rational World.
Divisibility in certain automorphism groups
We study solvability of equations of the form in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.
Embeddings into Simple Lattice-ordered Groups with Different First Order Theories.
Equivalence Systems with Finitely Many Relations.
Free actions of free groups on countable structures and property (T)
We show that if G is a non-archimedean, Roelcke precompact Polish group, then G has Kazhdan's property (T). Moreover, if G has a smallest open subgroup of finite index, then G has a finite Kazhdan set. Examples of such G include automorphism groups of countable ω-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation...
Graded morphisms of -modules
Let be finite dimensional -algebra which is a complete intersection, i.e. whith a regular sequences . Steve Halperin conjectured that the connected component of the automorphism group of such an algebra is solvable. We prove this in case is in addition graded and generated by elements of degree 1.
Green's L-relation for semigroups and compactifications.
Green's L-relation for semigroups and compactifications. (Short Communication).
Groupes de Lie p-adiques et ramification
Gyration numbers for involutions of subshifts of finite type II.