Related papers: Symmetrically complete ordered sets, abelian group…
We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear…
Let $G$ be a finite abelian group. For any positive integers $d$ and $m$, let $\varphi_G(d)$ be the number of elements in $G$ of order $d$ and $\mathsf M(G,m)$ be the set of all zero-sum sequences of length $m$. In this paper, for any…
In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…
The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…
We introduce the notions of proto-complete, complete, complete* and strong-complete objects in pointed categories. We show under mild conditions on a pointed exact protomodular category that every proto-complete (respectively complete)…
I show that one can explicitly construct topologically/geometrically distinguishable data which provide isomorphic copies (i.e. \emph{isomorphs}) of the tempered fundamental group of a geometrically connected, smooth, quasi-projective…
Inspired by an experimental study of energy-minimizing periodic configurations in Euclidean space, Cohn, Kumar and Sch\"urmann proposed the concept of formal duality between a pair of periodic configurations, which indicates an unexpected…
We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applications of our method to other problems, including the…
We show that if A is a linear order then Th(A) is either $\aleph_0$-categorical or Borel complete (in the sense of Friedman and Stanley). We generalize this; if A has countably many unary predicates attached, then Th(A) is…
We study the geometry of positive cones of left-invariant total orders (left-order, for short) in finitely generated groups. We introduce the \textit{Hucha property} and the \texit{Prieto property} for left-orderable groups. The first one…
Let $G$ be an $\ell$-group (which is short for ``lattice-ordered abelian group''). Baker and Beynon proved that $G$ is finitely presented iff it is finitely generated and projective. In the category $\mathcal U$ of {\it unital}…
We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of…
Let $\{G_i :i\in\N\}$ be a family of finite Abelian groups. We say that a subgroup $G\leq \prod\limits_{i\in \N}G_i$ is \emph{order controllable} if for every $i\in \mathbb{N}$ there is $n_i\in \mathbb{N}$ such that for each $c\in G$, there…
We consider the question of when sets definable in first-order expansions of groups contain the product of two infinite sets (we refer to this as the "productset property"). We first show that the productset property holds for any definable…
We study the synchronous and asynchronous automatic structures on the fundamental group of a graph of groups in which each edge group is finite. Up to a natural equivalence relation, the set of biautomatic structures on such a graph product…
We define and we characterize regular and c-regular cyclically ordered abelian groups. We prove that every dense c-regular cyclically ordered abelian group is elementarily equivalent to some cyclically ordered group of unimodular complex…
In this paper we consider the set of all bounded subsets of totally ordered Dedekind complete Riesz spaces, equipped with the order topology. We show the existence of bounded linear functions on this set, that are invariant under group…
In this paper, pointwise convergence, uniform convergence and compact convergence of sequences of holomorphic functions on an open subset of the complex plane are compared from a linear point of view. In fact, it is proved the existence of…
It is shown, for a given graph group $G$, that the fixed point subgroup Fix$\,\varphi$ is finitely generated for every endomorphism $\varphi$ of $G$ if and only if $G$ is a free product of free abelian groups. The same conditions hold for…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.