Related papers: Finite orbits of Hurwitz actions on braid systems

In this paper we study Thurston's automaton on the braid groups via binary operations. These binary operations are obtained from the construction of this automaton. We study these operations and find some connections between them in a "skew…

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions…

General bounds are presented for the diameters of orbital graphs of finite affine primitive permutation groups. For example, it is proved that the orbital diameter of a finite affine primitive permutation group with a nontrivial point…

We prove that two reflection factorizations of a parabolic quasi-Coxeter element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the same subgroup and have the same multiset of conjugacy classes. As a…

The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or…

We describe Artin's braid group on a (fixed) finite number of strings as a crossed module over itself. In particular, we interpret the braid relations as crossed module structure relations.

We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.

We study the bound states of brane/antibrane systems by examining the motion of a probe antibrane moving in the background fields of N source branes. The classical system resembles the point-particle central force problem, and the orbits…

It is shown that the restriction of the action of any group with finite orbit on the minimal sets of dendrites is equicontinuous. Consequently, we obtain that the action of any amenable group and Thompson group on dendrite restricted on…

In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions.…

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…

A free action of a finite group on an odd-dimensional sphere is said to be almost linear if the action restricted to each cyclic or 2-hyperelementary subgroup is conjugate to a free linear action. We begin this survey paper by reviewing the…

We deduce that the fundamental groups of the orbit configuration spaces of an effective and properly discontinuous action of a discrete group on a connected aspherical 2-manifold, with isolated fixed points, fit into a four-term exact…

We show that a finite unitary group which has orbits spanning the whole space is necessarily the setwise stabilizer of a certain orbit.

The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.

Motivated by the theory of Riemann surfaces, we classify all possibilities for finite simple groups acting faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most three fixed…

We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection…

We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has relatively few orbits? We prove that any field which has only…

We define the extremal length of elements of the fundamental group of the twice punctured complex plane and give upper and lower bounds for this invariant. The bounds differ by a multiplicative constant. The main motivation comes from…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.