Related papers: Some applications of augmentation quotients
We provide upper bounds for logarithmic torsion homology growth and Betti number growth of groups, phrased in the language of measured group theory.
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.
We introduce and study monomial ideals with regular quotients, which can be seen as an extension of monomial ideals with linear quotients. Based on these investigations, we are able to calculate the Betti numbers of toric ideals belonging…
We describe the fully residually F; or limit groups relative to F; (where F is a free group) that arise from systems of equations in two variables over F that have coefficients in F.
In this work the author studies the property close to property of order separability.
We give a review of some known published applications of quasigroups in cryptology.
For a group $G$, N-series $\cal G$ of $G$ and commutative ring $R$ let $I^n_{R,\cal G}(G)$, $n\ge 0$, denote the filtration of the group algebra $R(G)$ induced by $\cal G$, and $I_R(G)$ its augmentation ideal. For subgroups $H$ of $G$, left…
In this paper, we consider the relation between the group freeness and the amalgamated freeness of crossed product algebras.
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
We study the maximal ranks of a free and a free abelian quotients of a finitely generated group, called co-rank (inner rank, cut number) and the Betti number, respectively. We show that any combination of these values within obvious…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.
Free groups have many applications in Algebraic Topology. In this paper I specifically study the finitely generated free groups by using the covering spaces and fundamental groups. By the Van Kampen's theorem, we have a famous fact that the…
Under reasonable assumptions, a group action on a module extends to the minimal free resolutions of the module. Explicit descriptions of these actions can lead to a better understanding of free resolutions by providing, for example,…
We present a generalization of Warning's Second Theorem to polynomial systems over a finite local principal ring with suitably restricted input and output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
It has been established on many occasions that the set of quotients of prime numbers is dense in the set of positive real numbers. More recently, it has been proved that the set of quotients of primes in the Gaussian integers is dense in…
We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.
This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.
We apply the theory of Groebner bases to the computation of free resolutions over a polynomial ring, the defining equations of a canonically embedded curve, and the unirationality of the moduli space of curves of a fixed genus.