The archimedean graph of a positive function on a semigroup.
The arithmetic of curves defined by iteration
We show how the size of the Galois groups of iterates of a quadratic polynomial f can be parametrized by certain rational points on the curves Cₙ: y² = fⁿ(x) and their quadratic twists (here fⁿ denotes the nth iterate of f). To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality theorem...
The arithmetic theory of loop groups
The Artin exponent of finite groups
The ascending varietal chain of a variety of semigroups.
The asymptotic dimension of the first Grigorchuk group is infinity.
We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.
The Auslander-Reiten Graph of Integral Blocks with Cyclic Defect Two and Their Integral Representations.
The Auslander-Reiten Quiver of a Finite Group.
The Auslander-Reiten quiver of a modular group algebra revisited.
The Automorphism Group of a Class of Semi-Groups.
The automorphism group of a p-group of maximal class with an abelian maximal subgroup
The automorphism group of HNN extensions with finite base group
The automorphism group of some semigroups
The Automorphism Group of the Free Algebra of Rank Two
The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group...
The automorphism group of the graph of an R class.
The automorphism group of unary algebras.
The automorphisms of the orthogonal groups ... n (V), n ... 5.
The average order of a permutation.
The average rank of a product of transformations.
The averaged Dehn function relative to a given probability measure.