Inverse near permutation semigroups

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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.

Original languageEnglish
Pages (from-to)341-355
Number of pages15
JournalSemigroup Forum
Issue number3
Publication statusPublished - 1 Jan 2004


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