Chaotic group actions (Q5916339)

It is proved that there are no chaotic group actions on any topological space with a free arc. In this paper chaotic actions of groups of the type \(G\times F\), where \(F\) is a finite group, are studied. Under a suitable assumption, if \(F\) is cyclic group, then the topological space which admits a chaotic group action of \(\mathbb{Z}\times F\) must admit a chaotic homeomorphism. A topological space which admits a chaotic group action but no chaotic homeomorphisms is constructed.