Related papers: Enriched Herds And Finite Quantum Groupoids
In this note we show that groups with definable generics in a separably closed valued of finite imperfection degree can be embedded into groups definable in their algebraic closure.
To every group of $I$-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the…
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.
Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $\text{SL}_k(\mathbb{Z})$, for $k…
PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.
This paper deals with the vertex connectivity of enhanced power graph of finite group. We classify all abelian groups G such that vertex connectivity of enhanced power graph of G is 1. We derive an upper bound of vertex connectivity for the…
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
We prove that the invariably generating graph of a finite group can have an arbitrarily large number of connected components with at least two vertices.
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…
This paper is meant to be an informal introduction to Quantum Groups, starting from its origins and motivations until the recent developments. We call in particular the attention on the newly descovered relationship among quantum groups,…
We develop the theory of $H$-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of $H$-graded coverings of supermanifolds in the case where…
We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.
We present a sharp upper bound for the number of generators of a finite group in terms of the ratio between the order and the exponent.
We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture.
We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.
We consider the finite generation property for cohomology algebra of pointed finite tensor categories via de-equivariantization and exact sequence of finite tensor categories. As a result, we prove that all coradically graded pointed finite…
We study the problem of determining if the braid group representations obtained from quantum groups of types $E, F$ and $G$ at roots of unity have infinite image or not. In particular we show that when the fusion categories associated with…
We formulate the Gerstenhaber algebra structure of Hochschild cohomology of finite group extensions of some quantum complete intersections. When the group is trivial, this work characterizes the graded Lie brackets on Hochschild cohomology…