Abstract
For a semigroup S, p n ( S) denotes the number of n-ary term operations of S depending on all their variables. The purpose of this paper is to study finite semigroups S with the property that their p n -sequence p( S)=〈 p 0( S), p 1( S),…〉 is bounded. Such semigroups are described first in terms of identities and then structurally as nilpotent extensions of semilattices, Boolean groups and rectangular bands. As a corollary it is shown that if p( S) is bounded then eventually either p n ( S)=0 or 1. It is also shown that there is an effective procedure which decides whether the p n -sequence of a given finite semigroup is bounded or not.
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