Related papers: Orbit groups

There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation…

Let $X$ be a finite set such that $|X|=n$, and let $k< n/2$. A group is $k$-homogeneous if it has only one orbit on the sets of size $k$. The aim of this paper is to prove some general results on permutation groups and then apply them to…

For each prime p, we exhibit pairs of p-groups all of whose integral cohomology groups are isomorphic. The method used involves very little calculation. The groups are exhibited as kernels of homomorphisms from a compact Lie group G to…

In the paper the foundation of the $k$-orbit theory is developed. The theory opens a new simple way to the investigation of groups and multidimensional symmetries. The relations between combinatorial symmetry properties of a $k$-orbit and…

In this paper we describe orbits of automorphism group on a horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (may be non-normal) toric varieties a description…

By the work of Brodzki-Niblo-Nowak-Wright and Monod, topological amenability of a continuous group action can be characterized using uniformly finite homology groups or bounded cohomology groups associated to this action. We show that…

Let $G$ be a complex semisimple algebraic group and $X$ be a complex symmetric homogeneous $G$-variety. Assume that both $G$, $X$ as well as the $G$-action on $X$ are defined over real numbers. Then $G(\mathbb{R})$ acts on $X(\mathbb{R})$…

Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…

If $Q$ is a group acting as a group of automorphisms of another group $G$ (with finite orbits), denote by $C_*(G)^Q$ the subcomplex of $Q$-invariant chains in the bar complex $C_*(G)$. In this paper, we study the homology of the complex…

The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian $p$-group by a cyclic factor…

We associate to every quandle $X$ and an associative ring with unity $\mathbf{k}$, a nonassociative ring $\mathbf{k}[X]$ following [3]. The basic properties of such rings are investigated. In particular, under the assumption that the inner…

We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts ``like…

The description of the automorphism group of group $<a, b; [a^m,b^n]=1>$ ($m,n>1$) in terms of generators and defining relations is given. This result is applied to prove that any normal automorphism of every such group is inner.

In this paper, we study the structure of homogeneous subgroups of the homeomorphism group of the sphere, which are defined as closed groups of homeomorphisms of the sphere that contain the rotation group. We prove two structure theorems…

We consider orbit configuration spaces associated to finite groups acting freely by orientation preserving homeomorphisms on the $2$-sphere minus a finite number of points. Such action is equivalent to a homography action of a finite…

The P-matrix approach for the determination of the orbit spaces of compact linear groups enabled to determine all orbit spaces of compact coregular linear groups with up to 4 basic polynomial invariants and, more recently, all orbit spaces…

Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…

A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads…

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…

The orbifold braid groups of two dimensional orbifolds were defined in [1] (arXiv:math/9907194) to understand certain Artin groups as subgroups of some suitable orbifold braid groups. We studied orbifold braid groups in some more detail in…