Dense orbits of automorphisms and compactness of groups
This paper deals with the Halmos' question of whether locally compact groups which admit ergodic (under the Haar measure) automorphisms are compact. The question was solved in [\textit{M. Rajagopalan}, Proc. Am. Math. Soc. 17, 372-376 (1966; Zbl 0166.027), \textit{R. Kaufman} and \textit{M. Rajagapalan}, Mich. Math. J. 13, 373-374 (1966; Zbl 0156.262), \textit{T. S. Wu}, Math. Z. 96, 256-258 (1967; Zbl 0163.027), \textit{S. A. Yuzoinsij}, Russian Math. Surveys 22, 47-52 (1967)] with exception of the totally disconnected case, however had remained open for the exceptional case. The autor gives, by using the technique in dynamical systems, an answer for this case.
Halmos' question of whether locally compact groups which admit ergodic under the Haar measure automorphisms are compact
scientific article; zbMATH DE number 3906798
scientific article