Related papers: The quantum group fixing a sequence of finite subs…
We show that finite index quantum subgroups of a discrete quantum group are induced from finite index quantum subgroups of the unimodularization. As an application, we classify all finite index quantum subgroups of free products of the…
We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of $\mathbb{N}^{d}$ with finite complement in $\mathbb{N}^{d}$. These semigroups are affine semigroups, which in particular implies…
We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…
The order sequence of a finite group $G$ is a non-decreasing finite sequence formed of the element orders of $G$. Several properties of order sequences were studied by P. J. Cameron and H. K. Dey in a recent paper that concludes with a list…
We prove that given a fixed finite tree $P$, almost all trees contain $P$ as a subtree. Moreover, the inclusion can be made so that it induces an embedding of the corresponding (quantum) automorphism groups, thereby providing generic…
Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or…
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.
We have recently showed that it is possible to deal with collections of indistinguishable elementary particles (in the context of quantum mechanics) in a set-theoretical framework by using hidden variables, in a sense. In the present paper…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.
A collection of integer sequences is jointly ergodic if for every ergodic measure preserving system the multiple ergodic averages, with iterates given by this collection of sequences, converge in the mean to the product of the integrals. We…
We study an extension of Bernstein's theorem to the setting of quantum groups. For a d-tuple of free, identically distributed random variables we consider a problem of preservation of freeness under the action of a quantum subset of the…
We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure.
By using the structure and some properties of extraspecial and generalized/almost extraspecial $p$-groups, we explicitly determine the number of elements of specific orders in such groups. As a consequence, one may find the number of cyclic…
A major theme in arithmetic combinatorics is proving multiple recurrence results on semigroups (such as Szemer\'edi's theorem) and this can often be done using methods of ergodic Ramsey theory. What usually lies at the heart of such proofs…
We demonstrate how a generic automated theorem prover can be applied to establish the non-orderability of groups. Our approach incorporates various tools such as positive cones, torsions, generalised torsions and cofinal elements.
A key tool in recent advances in understanding arithmetic progressions and other patterns in subsets of the integers is certain norms or seminorms. One example is the norms on $\Z/N\Z$ introduced by Gowers in his proof of Szemer\'edi's…
We show that there is a sequence of subsets of each discrete Heisenberg group for which the non-singular ergodic theorem holds. The sequence depends only on the group; it works for any of its non-singular actions. To do this we use a metric…
We study the quantum automorphism group of the lexicographic product of two finite regular graphs, providing a quantum generalization of Sabidussi's structure theorem on the automorphism group of such a graph.
In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.