Related papers: Constructing and Deconstructing Group Actions

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

We examine the question of which finitely generated groups act properly on a finite product of simplicial trees, considering both arbitrary trees and where all trees are locally finite. In the second case we present evidence in favour of…

We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for 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.

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.

A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.

We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general…

This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially,…

This survey describes some recent work, by the authors and others, on the existence of algebraic fibrations of group extensions, as well as the finiteness properties of their algebraic fibers, in the realm of both abstract and pro-$p$…

We study the behaviour of infinitesimal deformation functors of local group actions with regard to passing to subgroups and quotient groups. Inspired by the cohomological information, we conjecture the existence of a decomposition of a…

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

A generalization of G-sets, called partial G-sets, are the sets that admit an action of partial maps on their subsets. Partial actions are a powerful tool to generalize many results of group actions. These generalizations are obtained by…

We introduce the concept of crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system.…

This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…

We study actions of finitely generated groups on $\bbR$-trees under some stability hypotheses. We prove that either the group splits over some controlled subgroup (fixing an arc in particular), or the action can be obtained by gluing…

We analyse the subgroup structure of direct products of groups. Earlier work on this topic has revealed that higher finiteness properties play a crucial role in determining which groups appear as subgroups of direct products of free groups…

The finite orbits of the braid group action on Stokes matrices are studied and are shown to be the orbits on ordered sets of reflections, generating finite groups. All invariants of a reflection arrangement are determined. Determination of…

We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on $M \times \bbS^{n_1} \times...\times \bbS^{n_k}$ for some…

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.

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