## Abstract

It is shown that the embeddability of a finite 4-nilpotent semigroup into a 0-simple finite semigroup with maximal groups from a pseudovariety Mathematical script capital V is decidable if and only if the universal theory of the class Mathematical script capital V is decidable. We show that it is impossible to replace 4 by 3 in this statement. We also show that if the membership in Mathematical script capital V is decidable then the membership in the pseudovariety generated by the class of all finite 0-simple semigroups with subgroups from Mathematical script capital V is decidable while the membership in the quasi-variety generated by this class of 0-simple semigroups may be undecidable.

Original language | English |
---|---|

Pages (from-to) | 75-96 |

Number of pages | 22 |

Journal | Journal of Pure and Applied Algebra |

Volume | 119 |

Issue number | 1 |

DOIs | |

State | Published - 2 Jun 1997 |

### Bibliographical note

Funding Information:* Corresponding author. E-mail: margolis@macs.biu.ac.il. ’ Supported in part by NSF grant DMS-9203981 and the Center for Communication University of Nebraska - Lincoln.