Geodesic
Small idempotent clones. I
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 1, pp. 105-118

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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].
Classification : 08A40, 08B05, 20M07, 20N02 
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     author = {Dudek, J\'ozef},
     title = {Small idempotent clones. {I}},
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Dudek, Józef. Small idempotent clones. I. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 1, pp. 105-118. http://geodesic.mathdoc.fr/item/CMJ_1998__48_1_a9/