Irreducibility of certain pseudovarieties 1 |
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| Authors: | S Margolis M Sapir P Weil |
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| Institution: | 1. Department of Mathematics and Computer Science , Bar Han University , Ramat Gan, 52900, Israel E-mail: margolis@bimacs.cs.biu.ac.il;2. Department of Mathematics and StatisticsCenter for Communic. and Inform , Science University of Nebraska-Lincoln , Lincoln, NE, 68588, USA E-mail: mvs@unlinfo.unl.edu;3. LIAFA , Université Pans- VI et CNRS , 4 place Jussieu, Paris Cedex 05, 75252, France E-mail: Pascal.Weil@litp.ibp.tz |
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| Abstract: | We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finii e semigroups are irreducible for join, for semidirect product and for Mal’cev product. In particular, these pseudovarieties do not admit maximal proper subpseudovarieties. More generally, analogous results are proved for the pseudovariety of all finite semigroups all of whose subgroups are in a fixed pseudovariety of groups H, provided th.it H is closed under semidirect product. |
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