Finite semigroups with few term operations

S Crvenkovic, I Dolinka, Nikola Ruskuc

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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) = <p0(S), p1(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. (C) 2001 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)205-214
Number of pages10
JournalJournal of Pure and Applied Algebra
Issue number2-3
Publication statusPublished - 23 Mar 2001




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