  Relationships between a chaotic behavior and closely related properties of
topological transitivity, sensitivity to initial conditions, density of closed
orbits of homeomorphism groups and their countable products are investigated.
We construct numerous new examples of chaotic groups of homeomorphisms of
countable products of various metrizable topological spaces, including
infinite-dimensional topological manifolds, whose factors can be as noncompact
surfaces, so triangulable closed manifolds of an arbitrary dimension.
