Amenable group actions on infinite graphs.
Amenable groups and cellular automata
We show that the theorems of Moore and Myhill hold for cellular automata whose universes are Cayley graphs of amenable finitely generated groups. This extends the analogous result of A. Machi and F. Mignosi “Garden of Eden configurations for cellular automata on Cayley graphs of groups” for groups of sub-exponential growth.
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...
Amenable, transitive and faithful actions of groups acting on trees
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.
An Abelian Quotient of the Mapping Class Group ...g.
An acyclic extension of the braid group.
An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221)
Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if . In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.
An addition theorem for finite semigroups.
An Addition Theorem for Some q-Hahn Polynomials.
An Addition Theorem in a Finite Abelian Group.
An algebraic characterization of geodetic graphs
We say that a binary operation is associated with a (finite undirected) graph (without loops and multiple edges) if is defined on and if and only if , and for any , . In the paper it is proved that a connected graph is geodetic if and only if there exists a binary operation associated with which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).
An algebraic characterization of multiplicative semigroups of real valued functions.
An algebraic characterization of quasi-Möbius homeomorphisms. (Une caractérisation algébrique des homéomorphismes quasi-Möbius.)
An algebraic functional equation
An algebraic proof of Isbell' s zigzag theorem.
An algebraic treatment of flow diagrams and its application to generalized recursion theory
An algorithm for finding the Veech group of an origami.
An algorithm for the decomposition of ideals of the group ring of a symmetric group.
An algorithm for the word problem in extensions and the dependence of its complexity on the group representation
An alternative proof of Hill's criterion of freeness for Abelian groups.