Related papers: Dimension quotients, Fox subgroups and limits of f…
We give a subexponential upper bound and a superpolynomial lower bound on the growth function of the Fabrykowski-Gupta group. As a consequence, we answer negatively a question by Longobardi, Maj and Rhemtulla about characterizing groups…
Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are natural extensions of previously published…
A Structure Theorem for Protori is derived for the category of finite-dimensional protori(compact connected abelian groups), which details the interplay between the properties of density, discreteness, torsion, and divisibility within a…
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
Let $R$ be an integral domain and $G$ be a subgroup of its group of units. We consider the category $\mathbf{\mathsf{Cob}}_G$ of 3-dimensional cobordisms between oriented surfaces with connected boundary, equipped with a representation of…
In this paper we study Fano threefolds with a torsion divisor (Fano--Enriques). Due to this torsion divisor, they can be described as quotients of Fano threefolds by a finite abelian group action. We start from lists of Fano threefolds by…
We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.
A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These…
The work is devoted to the extension groups in the category of functors from a small category to an additive category with an Abelian structure in the sense of Heller. It is constructed a spectral sequence which converges to the extension…
We show the connection between the relative Dehn function of a finitely generated metabelian group and the distortion function of a corresponding subgroup in the wreath product of two free abelian groups of finite rank. Further, we show…
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of…
This is the fourth and last paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. In it we finish the proof, analyzing limit groups obtained from other limit groups by adjoining roots. We generalize our…
We apply the geometric quantization procedure via symplectic groupoids proposed by E. Hawkins to the setting of epistemically restricted toy theories formalized by Spekkens. In the continuous degrees of freedom, this produces the algebraic…
It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the…
Based on the Riemann- and Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed…
In previous work, we defined the category of functors Fquad, associated to vector spaces over the field with two elements equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
We explicitly describe the Albanese morphism of a hyperelliptic variety, i.e., the quotient $X$ of an abelian variety $A$ by a finite group $G$ acting freely and not only by translations, by giving a description of the Albanese variety and…
We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the…
In his famous book, Felix Klein describes a complex variable for the quotients of the ordinary sphere by the finite groups of rotations and in particular for the most complex situation of the quotient by the symmetry group of the…