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Finite aperiodic semigroups with commuting idempotents and generalizations

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Abstract

It is proved that any pseudovariety of finite semigroups generated by inverse semigroups, the subgroups of which lie in some proper pseudovariety of groups, does not contain all aperiodic semigroups with commuting idempotents. In contrast we show that every finite semigroup with commuting idempotents divides a semigroup of partial bijections that shares the same subgroups. Finally, we answer in the negative a question of Almeida as to whether a result of Stiffler characterizing the semidirect product of the pseudovarieties ofR-trivial semigroups and groups applies to any proper pseudovariety of groups.

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Authors and Affiliations

  1. Mathematics Department, University of Essex, Wivenhoe Park, CO4 3SQ, Colchester, England

    Peter M. Higgins

  2. Department of Mathematics, Bar Ilan University, 52900, Ramat Gan, Israel

    Stuart W. Margolis

Authors
  1. Peter M. Higgins
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  2. Stuart W. Margolis
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Higgins, P.M., Margolis, S.W. Finite aperiodic semigroups with commuting idempotents and generalizations. Isr. J. Math. 116, 367–380 (2000). https://doi.org/10.1007/BF02773226

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