Abstract
Purchase PDF (559 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (0)
Purchase PDF (1377 K)
0. We say that 
doi:10.1016/0012-365X(95)00140-R 
Copyright © 1996 Published by Elsevier Science B.V.
Some combinatorial properties of infinite words and applications to semigroup theory*1
References and further reading may be available for this article. To view references and further reading you must purchase this article.
Received 31 August 1993;
Abstract
This paper is concerned with finiteness conditions for finitely generated semigroups. First, we present a combinatorial result on infinite sequences from which an alternative proof of a theorem of Restivo and Reutenauer follows: a finitely generated semigroup is finite if and only if it is periodic and permutable. Then, generalizing notions studied in some papers of de Luca, Restivo, Hashiguchi and Varricchio, we introduce the notion of ω-iteration property and we prove that a finitely generated semigroup has the ω-iteration property if and only if it is finite.
Article Outline
*1 A preliminary version of this paper has appeared in Proceedings of the 5th Conference ‘Formal Power Series and Algebraic Combinatorics’ (Firenze, 21–25 June 1993) under the title ‘Ultimately periodic and n-divided words’.
