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Groups admitting ergodic actions with generalized discrete spectrum. (English) Zbl 0399.22005
The class of groups admitting an effective ergodic action with generalized discrete spectrum is a natural generalization of the class of maximally almost periodic groups. H. Freudenthal has given a complete characterization of the connected maximally almost periodic groups, and here we give a complete characterization of the almost connected groups admitting an effective ergodic action with generalized discrete spectrum. Namely, we show that an almost connected group is in this class if and only if it is type R. It is known that this is equivalent to the group being of polynomial growth, and for Lie groups is just the condition that all eigenvalues of the adjoint representation lie on the unit circle.
Reviewer: Calvin C. Moore

22D40 Ergodic theory on groups
28D15 General groups of measure-preserving transformations
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