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Abstract
A formula for the rank of an arbitrary finite completely 0simple semigroup, represented as a Rees matrix semigroup M0[G ; I , Lambda; P], is given. The result generalizes that of Ruskuc concerning the rank of connected finite completely 0simple semigroups. The rank is expressed in terms of vertical bar I vertical bar, vertical bar Lambda vertical bar, 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 onetoone 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 }).
Original language  English 

Pages (fromto)  46574678 
Journal  Communications in Algebra 
Volume  33 
Issue number  12 
DOIs  
Publication status  Published  2005 
Keywords
 0simple semigroups
 minimal generating sets
 rank
 RANK
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Dive into the research topics of 'Generating sets of completely 0simple semigroups'. Together they form a unique fingerprint.Projects
 1 Finished

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications
Linton, S. A., Gent, I. P., Leonhardt, U., Mackenzie, A., Miguel, I. J., Quick, M. & Ruskuc, N.
1/09/05 → 31/08/10
Project: Standard