On loxodromic actions of Artin–Tits groups

All discrete RP groups with non-π-loxodromic generators

In this paper we give necessary and sufficient conditions for discreteness of a group generated by a hyperbolic element and an elliptic one of odd order with intersecting axes. This completes classification of the discrete groups with non-π-loxodromic generators in the class of twogenerator groups with real parameters. The criterion is given also as a list of all parameters that correspond to d...

Actions of Groups on Lattices

The aim of this paper is to study the actions of the groups on lattices and to give some connections between the structure of a group and the structure of its subgroup lattice. Moreover, we shall introduce the concept of direct ∨-sum of G-sublattices and we shall present a generalization of a result about finite nilpotent groups. 1 Preliminaries Let (G, ·, e) be a monoid and L be a G–set (relat...

On minimal actions of Polish groups

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked whether such groups exist, and a negative answer to a problem of R. Ellis on the isomorphism of L(G), the universal point transitive G-system (for discrete G this is the same as PG the Stonetech compacti...

Partial Actions of Groups on Cell Complexes

Expansiveness of algebraic actions on connected groups

Any such neighborhood is called an expansive neighborhood of the identity in X. An automorphism τ of X is said to be expansive if the cyclic group generated by τ acts expansively on X. It is easy to check that when X is compact and ρ is an endomorphism action of a semigroup Γ, these two notions of expansiveness coincide. The notion of expansiveness plays an important role in the study of dynami...