相关论文: Commutative decomposition of infinite symmetric gr…

We say that a group $G$ has Bergman's property (the property of universality of finite width) if for every generating set $X$ of $G$ with $X=X^{-1}$ we have that $G=X^k$ for some natural number $k.$ The property is named after George…

In 2012 Monod introduced examples of groups of piecewise projective homeomorphisms which are not amenable and which do not contain free subgroups, and later Lodha and Moore introduced examples of finitely presented groups with the same…

In this paper we answer a question of Gabriel Navarro about orbit sizes of a finite linear group H acting completely reducibly on a vector space V: if the orbits containing the vectors a and b have coprime lengths m and n, we prove that the…

For a fixed finite solvable group $G$ and number field $K$, we prove an upper bound for the number of $G$-extensions $L/K$ with restricted local behavior (at infinitely many places) and ${\rm inv}(L/K)<X$ for a general invariant $"{\rm…

In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid $\mathbb{N} ^ \mathbb{N}$ or the symmetric inverse monoid $I_{\mathbb{N}}$ with their respective canonical…

If a group $G$ is the union of proper subgroups $H_1, \dots, H_k$, we say that the collection $\{H_1, \dots H_k \}$ is a cover of $G$, and the size of a minimal cover (supposing one exists) is the covering number of $G$, denoted…

In the paper we obtain some new upper bounds for exponential sums over multiplicative subgroups G of F^*_p having sizes in the range [p^{c_1}, p^{c_2}], where c_1,c_2 are some absolute constants close to 1/2. As an application we prove that…

In arXiv:1303.1129, the authors provided a bound for the palindromic width of free abelian-by-nilpotent group $AN_n$ of rank $n$ and free nilpotent group ${\rm N}_{n,r}$ of rank $n$ and step $r$. In the present paper we study palindromic…

We show that the wreath product $G \wr \mathbb{Z}^n$ of any finitely generated group $G$ with $\mathbb{Z}^n$ has finite palindromic width. We also show that $C \wr A$ has finite palindromic width if $C$ has finite commutator width and $A$…

For a positive integer $k$, a group $G$ is said to be totally $k$-closed if for each set $\Omega$ upon which $G$ acts faithfully, $G$ is the largest subgroup of $\mathrm{Sym}(\Omega)$ that leaves invariant each of the $G$-orbits in the…

Starting with a highest weight representation of a Kac-Moody group over the complex numbers, we construct a monoid whose unit group is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We…

Starting with a highest weight representation of a Kac-Moody group over the complex numbers, we construct a monoid whose unit group is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We…

The strong symmetric genus of a finite group is the minimum genus of a compact Riemann surface on which the group acts as a group of automorphisms preserving orientation. A characterization of the infinite number of groups with strong…

We investigate complement-finite submonoids of the monoid of nonnegative integer points of a unipotent linear algebraic group $G$. These monoids are in general noncommutative but they specialize to the generalized numerical monoids of…

We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We…

In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More precisely, for each prime number $p$ there is a family…

We study invariant and bi-invariant metrics on groups focusing on finite groups $G$. We show that non-equivalent (bi) invariant metrics on $G$ are in 1-1 correspondence with unitary symmetric (conjugate) partitions on $G$. To every metric…

We investigate additive properties of sets $A,$ where $A=\{a_1,a_2,\ldots ,a_k\}$ is a monotone increasing set of real numbers, and the differences of consecutive elements are all distinct. It is known that $|A+B|\geq c|A||B|^{1/2}$ for any…

For a sequence $S$ over a finite abelian group, let $MZ(S)$ denote the length of the shortest nonempty zero-sum subsequence of $S$. We prove that if $G$ is finite abelian of order $n$ and $S$ has length $n$, then $MZ(S)\le n-|\supp(S)|+1$.…

The Ehresmann-Schein-Nambooripad theorem gives a structure theorem for inverse monoids: they are inductive groupoids. A particularly nice case due to Jarek is that commutative inverse monoids become semilattices of abelian groups. It has…