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Summary:
G. Grätzer and A. Kisielewicz devoted one section of their survey paper concerning $p_n$-sequences and free spectra of algebras to the topic “Small idempotent clones” (see Section 6 of [18]). Many authors, e.g., [8], [14, 15], [22], [25] and [29, 30] were interested in $p_n$-sequences of idempotent algebras with small rates of growth. In this paper we continue this topic and characterize all idempotent groupoids $(G,\cdot )$ with $p_2(G,\cdot )\le 2$ (see Section 7). Such groupoids appear in many papers see, e.g. [1], [4], [21], [26, 27], [25], [28, 30, 31, 32] and [34].
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