相关论文: Some properties of finite meadows

This paper surveys basic properties of finite presentation in groups, Lie algebras and rings. It includes some new results and also new, more elementary proofs, of some results that are already in the literature. In particular, we discuss…

A finite EI category is a small category with finitely many morphisms such that every endomorphism is an isomorphism. They include finite groups, finite posets and free categories of finite quivers as special cases. In this paper we…

We show that the class of finite rooted binary plane trees is a Ramsey class (with respect to topological embeddings that map leaves to leaves). That is, for all such trees P,H and every natural number k there exists a tree T such that for…

This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.

Let $\mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with…

We present a characterization of the finite groups in which all real classes have prime powers size.

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

A monotone grid class is a permutation class (i.e., a downset of permutations under the containment order) defined by local monotonicity conditions. We give a simplified proof of a result of Murphy and Vatter that monotone grid classes of…

This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the…

The finite basis property is often connected with the finite rank property, which it entails. Many examples have been produced of finite rank varieties which are not finitely based. In this note, we establish a result on nilpotent…

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…

We present new classes of permutation polynomials over finite fields.

This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the…

The purpose of this note is to give a self contained description of Walls finiteness obstruction.

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…