Abstract
In this paper, among other results, we prove that a clone C with five essentially binary operations is minimal if and only if C is a clone of a non-trivial affine space over GF(7). This result is a product of systematic investigation of varieties of idempotent commutative groupoids. It is probably the most spectacular result of this investigation, but many other results formulated and proved throughout the paper may turn out more useful in further study in this area.
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