Semigroup Forum

, 76:579 | Cite as

The idempotent-separating degree of a block-group

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Abstract

In this note we characterize the least positive integer n such that there exists an idempotent-separating homomorphism from a finite block-group S into the monoid of all partial transformations of a set with n elements. In particular, as for a fundamental semigroup S this number coincides with the smallest size of a set for which S can be faithfully represented by partial transformations, we obtain a generalization of Easdown’s result established for fundamental finite inverse semigroups.

Keywords

Block-groups Representations Transformations 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Departamento de Matemática, F.C.T.Universidade Nova de LisboaMonte da CaparicaPortugal
  2. 2.Centro de ÁlgebraUniversidade de LisboaLisboaPortugal

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