Related papers: Chain conditions in dependent groups
In this note we study a class of finite groups for which the orders of subgroups satisfy a certain inequality. In particular, characterizations of the well-known groups $\mathbb{Z}_2\times\mathbb{Z}_2$ and $S_3$ are obtained.
We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…
This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is…
We consider the capability of $p$ groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition…
The 2-categories of strict 2-groups and crossed modules are introduced and their 2-equivalence is made explicit.
We prove that every \omega-categorical, generically stable group is nilpotent-by-finite and that every \omega-categorical, generically stable ring is nilpotent-by-finite.
We prove the ascending chain condition for log canonical thresholds of bounded coregularity.
Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.
The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We review criteria for transience and weak…
In this paper, we determine new characterizations of nested and nested GVZ-groups, including character-free characterizations, but we additionally show that nested groups and nested GVZ-groups can be defined in terms of the existence of…
We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…
We present type $\theta$ Stokes' theorem for type $\theta$ $k$-chains which extends the fundamental theorem of calculus in higher dimensions.
In this paper, we have studied the axiomatics of {\it Ann-categories} and {\it categorical rings.} These are the categories with distributivity constraints whose axiomatics are similar with those of ring structures. The main result we have…
We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each $n> 3$ a family of $n$…
In the framework of the Time Dependent Scattering Theory we discuss three forms of Cluster Separability as well as the conditions for the representation of the scattering system dynamics implied by their respective use.
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…
We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the…
We show that in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. We also…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.