Related papers: Solubility of groups can be characterized by confi…
We prove a new criterion for the solvability of the finite groups, depending on the function $\psi_k(G)$ which is defined as the sum of $k$-th powers of the element orders of $G$. We show that our result can be used to show the solvability…
The aim of this article is to define a notion of cardinal utility function called measurable utility and to define it on a connected and separable subset of a weakly ordered topological space. The definition is equivalent to the ones given…
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…
We extend the classical notion of solvability to a lambda-calculus equipped with pattern matching. We prove that solvability can be characterized by means of typability and inhabitation in an intersection type system P based on…
Let G be a possibly disconnected reductive group over a finite field with Frobenius map F. The main result of this paper is that the characteristic functions af "admissible complexes" A on G such that F^*A is isomorphic to A form a basis of…
There exist combable groups in which the conjugacy problem is unsolvable. The isomorphism problem is unsolvable for certain recursive sequences of finite presentations of combable groups.
We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…
We provide a pure algebraic version of the dynamical characterization of Conrad's property. This approach allows dealing with general group actions on totally ordered spaces. As an application, we give a new and somehow constructive proof…
We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions
We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is essentially produced from a sofic approximation. This…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific…
We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will allow us to obtain a canonical way in which to assign ideals…
We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their…
We continue the study of a class of topological $\mathcal{L}$-fields endowed with a generic derivation $\delta$, focussing on describing definable groups. We show that one can associate to an $\mathcal{L}_{\delta}$ definable group a type…
A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…
Erling Folner proved that the amenability or nonamenability of a countable group depends on the complexity of its finite subsets. Complexity has three measures: maximum Folner ratio, optimal cooling function, and minimum cooling norm. Our…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $\sigma$-finite measure spaces. It is inspired by the very first definition of amenability,…