Vol. 38, No. 1, 1971

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Ergodic automorphisms and affine transformations of locally compact groups

M. Rajagopalan and Bertram Manuel Schreiber

Vol. 38 (1971), No. 1, 167–176

It has been conjectured that if a locally compact group G has a continuous automorphism which is ergodic with respect to Haar measure then G must be compact. This is true when G is commutative or connected. In this paper further results in support of this conjecture are presented. In particular, it is shown that the problem can be reduced to the consideration of compactly generated, totally disconnected, locally compact groups without compact, open, normal subgroups and that the conjecture holds for many automorphisms of a certain class of such groups. Finally, the structure of locally compact groups which admit ergodic affine transformations is investigated.

Mathematical Subject Classification 2000
Primary: 28A65
Secondary: 22D05, 22D40
Received: 6 July 1970
Published: 1 July 1971
M. Rajagopalan
Bertram Manuel Schreiber