相关论文: Direct and Central Products of Localities

We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.

We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.

We show that the product of two partial normal subgroups of a locality (in the sense of Chermak) is again a partial normal subgroup. This generalizes a theorem of Chermak and fits into the context of building a local theory of localities.

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

In this article, we study group theoretical embedding properties of subgroups in central products of finite groups. Specifically, we give characterizations of normal, subnormal, and abnormal subgroups of a central product of two groups.

We investigate connections between local tameness of a group and a number of its ends.

In this paper, we have studied the loops which are the semidirect products of a loop and a group. Also, the cummutant, nuclei and the center of such loops are studied.

The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…

We present some constructions of groupoids as: direct product, semidirect product, and we give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient…

This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats two-parameter semigroups, and contains also contributions to dilation theory of product system representations. The…

We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of…

Let $G_{2}$ be a group which acts trivially on an abelian group $G_{1}$. As is well known, each perturbed direct product of $G_{1}$ and $G_{2}$ under a 2-cocycle $\varepsilon\in Z^{2}(G_{2},G_{1})$ determines a central extension of $G_{1}$…

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…

The theory of saturated fusion systems resembles in many parts the theory of finite groups. However, some concepts from finite group theory are difficult to translate to fusion systems. For example, products of normal subsystems with other…

In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…

This paper continues the development of the theory of finite localities that was begun in "Finite Localities I". The emphasis in this Part 2.

We survey some results concerning finite group actions on products of spheres.

We characterize the situations in which certain accumulation properties of topological spaces are preserved under taking products.

We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.

This paper concerns partial groups, objective partial groups, and (finite) localities, with special attention given to the quotient of a locality by a partial normal subgroup.