Homological methods in group theory, permutations of infinite set, automorphisms of infinite dimensional Hilbert space, Eilenberg-MacLane homology, Article, 510.mathematics, acyclic groups, group of linear automorphisms of infinite dimensional vector space, General groups of measure-preserving transformations, Infinite automorphism groups, Noncommutative dynamical systems, measure preserving automorphisms of Lebesgue measure space