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In Organic Chemistry by Clayden et al., the following reaction is shown:

Diastereoselective cyclopropanation of cyclohex-3-en-1-ol

The cyclopropane ring is formed on the same side as the alcohol group. Is this because of the interaction between Zn and the OH group, which directs the reagent to approach from the same side as the OH group?

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Yes. Right after Clayden mentions this stereoselectivity, he proceeds to state that this is due to "coordination between the zinc atom and the hydroxyl group in the transition state" (pp. 1067-8, 1st ed):

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