The First Orlicz Cohomology of General Discrete Groups

We study the first Orlicz cohomology of general (not necessarily countable) discrete groups, based on the methods developed by Eastridge and other authors for ℓ^p-cohomology and our previous study of Orlicz cohomology. Some conditions are given for the triviality of the first ℓ^Φ-cohomology and reduced ℓ^Φ-cohomology of a discrete group and for the coincidence of these spaces.