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A class of strictly ergodic Toeplitz flows with positive entropies and trivial topological centralizers is presented.
The topological centralizers of Toeplitz flows satisfying a condition (Sh) and their Z-extensions are described. Such Toeplitz flows are topologically coalescent. If {q, q, ...} is a set of all except at least one prime numbers and I, I, ... are positive integers then the direct sum ⊕
Z ⊕ Z can be the topological centralizer of a Toeplitz flow.
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