Related papers: Spherically orderable groups

We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

We wrote this paper as an example to show the way we pass from ordered semigroups to ordered hypersemigroups.

Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…

The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in nature - are given and shown to lead to the same objects.…

In this work the author studies the property close to property of order separability.

Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…

We define and study the Picard group of a monoid scheme and the class group of a normal monoid scheme. To do so, we develop some ideal theory for (pointed abelian) noetherian monoids, including primary decomposition and discrete valuations.…

We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of…

In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

The order sequence of a finite group $G$ is a non-decreasing finite sequence formed of the element orders of $G$. Several properties of order sequences were studied by P. J. Cameron and H. K. Dey in a recent paper that concludes with a list…

In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

Skew idempotent functionals of ordered semirings are studied. Different associative and non-associative semirings are considered. Theorems about properties of skew idempotent functionals are proved. Examples are given.

Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…

By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the…

These are expanded notes from lectures on the geometry of spherical varieties given in Sanya. We review some aspects of the geometry of spherical varieties. We first describe the structure of $B$-orbits. Using the local structure theorems,…