相关论文: On generating sets of infinite symmetric group

In this paper we bring together results about the density of subsemigroups of abelian Lie groups, the minimal number of topological generators of abelian Lie groups and a result about actions of algebraic groups. We find the minimal number…

We sketch a simplification of proofs of old results on the arithmeticity of the group generated by opposing integral unipotent radicals in higher rank arithmetic groups

We continue the study of how one can define means of infinite sets. We introduce many new properties, investigate their relations to each other and how they can typify a mean. We collect the properties in property groups e.g. for…

We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…

The generating graph encodes how generating pairs are spread among the elements of a group. For more than ten years it has been conjectured that this graph is connected for every finite group. In this paper, we give evidence supporting this…

We construct infinitely many signed graphs having symmetric spectrum, by using the NEPS and rooted product of signed graphs. We also present a method for constructing large cospectral signed graphs. Although the obtained family contains…

The plane Cremona group over the finite field $\mathbb{F}_2$ is generated by three infinite families and finitely many birational maps with small base orbits. One family preserves the pencil of lines through a point, the other two preserve…

A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…

We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…

We study groups generated by sets of pattern avoiding permutations. In the first part of the paper we prove some general results concerning the structure of such groups. In the second part we carry out a case-by-case analysis of groups…

It is a well-known open problem since the 1970s whether a finitely generated perfect group can be normally generated by a single element or not. We prove that the topological version of this problem has an affirmative answer as long as we…

We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.

Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…

New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…

We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.

Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and…

Let $S(\infty)$ denote the infinite symmetric group formed by the finitary permutations of the set of natural numbers; this is a countable group. We introduce its virtual group algebra, a completion of the conventional group algebra…

Let $I$ be an arbitrary ideal generated by binomials. We show that certain equivalence classes of fibers are associated to any minimal binomial generating set of $I$. We provide a simple and efficient algorithm to compute the indispensable…