Semigroup Forum

, Volume 69, Issue 3, pp 446–456 | Cite as

Permutative Semigroups Whose Congruences Form a Chain

  • A. NagyEmail author
  • Peter R. JonesEmail author


Semigroups whose congruences form a chain are often termed Δ-semigroups. The commutative Δ-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative Δ-semigroups. It turns out that there are only six noncommutative examples, each of which has at most three elements.


Natural Generalization Permutational Identity Permutative Semigroup 
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Copyright information

© Springer Science + Business Media Inc. 2004

Authors and Affiliations

  1. 1.Department of Algebra Institute of Mathematics, Budapest University of Technology and Economics, 1521 Budapest, Pf. 91 Hungary
  2. 2.Department of Mathematics, Statistics and Computer Science, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881USA

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