Topological equivalence of Haar measures on compact groups

The existence of homeomorphisms establishign an isometry of normalized Haar measures on (metrizable) compact groups is studied. In the case of 0-dimensional groups, a complete answer is given in terms of the indices of open normal subgroups. For example, for the countable powers of the groups ℤ/(m) and ℤ/(n), the answer is affirmative if and only ifm andn have the same prime divisors. A certain class of extensions of 0-dimensional groups is also studied. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 188–194, August, 2000.