We construct a simple transformation whose centralizer is isomorphic to (ℭ)2 ⋊ A ℭ, where A is an aperiodic automorphism of ℭ2. As a corollary we obtain an example of a ℭ2-action with minimal self-joinings which is conjugate to the (twisted by A) action . This answers a question of E. Glasner.
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