Abstract
Let ℒk (3 ≦ k < ℵ0) denote the lattice of clones of finitary operations on a k-element set. One interesting characteristic of the uncountable lattice ℒk is the minimum lk of the cardinalities of maximal chains in ℒk. It is known that for k prime lk = 5. In this paper the 5-element maximal chains contained in ℒk are investigated. It is proved that for k composite lk ≧ 6 while for k prime there are exactly (k–2)! (k + 4) 5-element maximal chains in ℒk, each closely related to a group operation.
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