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Communications in Algebra Volume 32, 2004 - Issue 7
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Original Articles

Rank and Status in Semigroup Theory

Alessandra Cherubini Dipartimento di Matematica, Politecnico di Milano, Milano, Italy; Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano, ItalyCorrespondence[email protected]
,
John M. Howie Mathematical Institute, University of St. Andrews, North Haugh, St. Andrews, Fife, UK
&
Brunetto Piochi Dipartimento di Matematica “U. Dini”, Università degli Studi di Firenze, Firenze, Italy
Pages 2783-2801 | Received 01 Jan 2003, Accepted 01 Jul 2003, Published online: 18 Aug 2006
 
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Abstract

For each generating set A of a finite semigroup S the integer Δ(A) is defined as the least n for which every element of S is expressible as a product of at most n elements of A. The status of S is defined as the least value of |A|Δ(A) among generating sets of A. Some general bounds are obtained, and the notion is explored in more detail for certain well understood classes of semigroups.

1991 Mathematics Subject Classification:

Acknowledgments

Notes

#Communicated by P. Higgins.

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