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Inverse Near Permutation Semigroups

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Abstract

A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group G of permutations on N elements and by a set H of transformations of rank N - 1. In this paper we give necessary and sufficient conditions for a near permutation semigroup S = ‹G,H›, where H is a group, to be inverse. Moreover, we obtain conditions which guarantee that its semilattice of idempotents is generated by the idempotents of S of rank greater than N - 2 or N - 3.

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Authors and Affiliations

  1. Centro de Algebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal and Departamento de Matematica, Faculdade de Ciencias e Tecnologia da Universidade Nova de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal

    Jorge M. André

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  1. Jorge M. André
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Correspondence to Jorge M. André.

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André, J. Inverse Near Permutation Semigroups. Semigroup Forum 69, 331–355 (2004). https://doi.org/10.1007/s00233-004-0122-4

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  • DOI: https://doi.org/10.1007/s00233-004-0122-4

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