Related papers: Group-like Uninorms
In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both…
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each…
For a certain class of Lie bialgebras $(A,A^*)$ the corresponding quantum universal enveloping algebras $U_q(A)$ are prooved to be equivalent to quantum groups Fun$_q(F^*)$, $F^*$ being the factor group for the dual group $G^*$. This…
Using a categorial version of Fra\"iss\'e's theorem due to Droste and G\"obel, we derive a criterion for a comma-category to have universal homogeneous objects. As a first application we give new existence result for universal structures…
In 1959, P. Hall introduced the locally finite group $\mathcal{U}$, today known as Hall's universal group. This group is countable, universal, simple, and any two finite isomorphic subgroups are conjugate in $\mathcal{U}$. It can be…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
The idempotent problem of a finitely generated inverse semigroup is the formal language of all words over the generators representing idempotent elements. This note proves that a finitely generated inverse semigroup with regular idempotent…
An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the literature. It is developed using many varied examples, with a…
Unitary designs are essential tools in several quantum information protocols. Similarly to other design concepts, unitary designs are mainly used to facilitate averaging over a relevant space, in this case, the unitary group…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there…
We show that there is an order-preserving embedding of the additive group of rational numbers $\mathbb{Q}$ into a 2-generator group $G$. The group $G$ can be chosen to be a solvable group $G$ of length 3, which is a minimal result in the…
We investigate the possible structures imposed on a finite group by its possession of an automorphism sending a large fraction of the group elements to their cubes, the philosophy being that this should force the group to be, in some sense,…
We lay down the fundations of the theory of groups of finite Morley rank in which local subgroups are solvable and we proceed to the local analysis of these groups. We prove the main Uniqueness Theorem, analogous to the Bender method in…
General arguments of Baumslag and Bieri guarantee that any metabelian group of finite Pr\"ufer rank can be embedded in a metabelian constructible group. Here, we consider the metric behavior of a rich class of examples and analyze the…
Every countable group that does not contain a finitely generated subgroup of exponential growth imbeds in a finitely generated group of subexponential growth. This produces in particular the first examples of groups of subexponential growth…
Inspired by Lurie's theory of quasi-unital algebras we prove an analogous result for $\infty$-categories. In particular, we show that the unital structure of an $\infty$-category can be uniquely recovered from the underlying non-unital…
We introduce and study some families of groups whose irreducible characters take values on quadratic extensions of the rationals. We focus mostly on a generalization of inverse semi-rational groups, which we call uniformly semi-rational…
Methods from additive number theory are applied to construct families of finitely generated linear semigroups with intermediate growth.