Relations between clones and full monoids

摘要

An endoprimal clone is defined via a set of unary operations. Itwas known before that the endoprimal clone for the setO₄⁽¹⁾ of all unary operations on, a k-element setis the least clone J_k and that the endoprimal clone for thesymmetric group S_k strictly includes J_k. In thispaper we consider monoids of unary operations and clones correspondingto such monoids. We define a descending sequence {N_i}_i=1^k=1 of monoids lying betweenO_k⁽¹⁾ and S_k, and show that theendoprimal clone for N_k-1 is distinct from J_k.Finally we present a characterization of the endoprimal clone forS_k