Generating Sets of Completely 0-Simple Semigroups |
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| Authors: | R. Gray N. Ruškuc |
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| Affiliation: | 1. Mathematical Institute , University of St. Andrews, North Haugh , St. Andrews, Fife, UK robertg@mcs.st-and.ac.uk;3. Mathematical Institute , University of St. Andrews, North Haugh , St. Andrews, Fife, UK |
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| Abstract: | ABSTRACT A formula for the rank of an arbitrary finite completely 0-simple semigroup, represented as a Rees matrix semigroup ?0[G; I, Λ; P], is given. The result generalizes that of Ru?kuc concerning the rank of connected finite completely 0-simple semigroups. The rank is expressed in terms of |I|, |Λ|, the number of connected components k of P, and a number r min, which we define. We go on to show that the number r min is expressible in terms of a family of subgroups of G, the members of which are in one-to-one correspondence with, and determined by the nonzero entries of, the components of P. A number of applications are given, including a generalization of a result of Gomes and Howie concerning the rank of an arbitrary Brandt semigroup B(G,{1,…,n}). |
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| Keywords: | 0-simple semigroups Minimal generating sets Rank |
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