Related papers: On some examples of group actions and group extens…

We investigate Moufang loops which can be written as the semidirect product of a loop and a group. We also examine a particular class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms…

We consider the action of a parabolic subgroup of the General Linear Group on a metabelian ideal. For those actions, we classify actions with finitely many orbits using methods from representation theory.

A framework for higher gauge theory based on a 2-group is presented, by constructing a groupoid of connections on a manifold acted on by a 2-group of gauge transformations, following previous work by the authors where the general notion of…

We show sufficient criteria for a group of homeomorphisms acting on a metric space X to extend to one acting on a given compactification of X. We give examples for when this can fail when one of the criteria is not met.

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

In this review we present some recent extensions of the method of the weakly conjugate operator. We illustrate these developments through examples of operators on graphs and groups.

We construct a central extension of the group of automorphisms of a 2-Tate vector space viewed as a discrete 2-group. This is done using an action of this 2-group on a 2-gerbe of gerbel theories. This central extension is used to define…

A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…

In our present investigation we propose to study and develop the I-function of two variables analogous to the I-function of one variable introduced and studied by one of the authors[24]. The conditions for convergence, series…

These are introductory notes on some aspects of concentration of measure in the presence of an acting group and its links to Ramsey theory.

We associate a 2-complex to the following data: a presentation of a semigroup $S$ and a transitive action of $S$ on a set $V$ by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex.…

In this paper we present Cohen-Montgomery-type duality theorems for groupoid (co)actions.

We study constructions of groups, in particular of groups of intermediate rank, which are accessible to surgery techniques.

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…

The aim of the article is to study the extension theory of gyrogroups under certain conditions. Consequently, we see that there is an equivalence between the category GEXT of group-gyro extensions and the category GFAC of group-gyro factor…

We give the basic definitions of group actions on (algebraic) stacks, and prove the existence of fixed points and quotients as (algebraic) stacks.

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

Some well-known and less well-known or new notions related to group actions are surveyed. Some of these notions are used to generalize affine spaces. Actions are seen as functions with values in transformation monoids

Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p-ranks of the class groups Cl(K) and Cl(k).

Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…