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Finite basis problem for semigroups of order six

Part of: Semigroups

Published online by Cambridge University Press:  01 January 2015

Edmond W. H. Lee  and
Wen Ting Zhang
Edmond W. H. Lee
Affiliation:
Division of Math, Science, and Technology, Nova Southeastern University, Fort Lauderdale, FL 33314, USA email [email protected]
Wen Ting Zhang
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou, Gansu 730000, PR China email [email protected]

Abstract

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Two semigroups are distinct if they are neither isomorphic nor anti-isomorphic. Although there exist $15\,973$ pairwise distinct semigroups of order six, only four are known to be non-finitely based. In the present article, the finite basis property of the other $15\,969$ distinct semigroups of order six is verified. Since all semigroups of order five or less are finitely based, the four known non-finitely based semigroups of order six are the only examples of minimal order.

MSC classification

Primary: 20M05: Free semigroups, generators and relations, word problems
Secondary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 1 - 129
Copyright
© The Author(s) 2015 

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