Algorithmic problems for finite groups and finite 0-simple semigroups

T. E. Hall; S. I. Kublanovskii; S. Margolis; M. V. Sapir; P. G. Trotter

doi:10.1016/s0022-4049(96)00050-3

Algorithmic problems for finite groups and finite 0-simple semigroups

T. E. Hall
, S. I. Kublanovskii
, S. Margolis
, M. V. Sapir
, P. G. Trotter

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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	https://doi.org/10.1016/s0022-4049(96)00050-3
State	Published - 2 Jun 1997

Bibliographical note

Funding Information:
* Corresponding author. E-mail: [email protected]. ’ Supported in part by NSF grant DMS-9203981 and the Center for Communication University of Nebraska - Lincoln.

Funding

* Corresponding author. E-mail: [email protected]. ’ Supported in part by NSF grant DMS-9203981 and the Center for Communication University of Nebraska - Lincoln.

Funders	Funder number
Center for Communication University of Nebraska
National Science Foundation	DMS-9203981
Directorate for Mathematical and Physical Sciences	9203981

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10.1016/s0022-4049(96)00050-3

Cite this

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title = "Algorithmic problems for finite groups and finite 0-simple semigroups",

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.",

author = "Hall, \{T. E.\} and Kublanovskii, \{S. I.\} and S. Margolis and Sapir, \{M. V.\} and Trotter, \{P. G.\}",

note = "Funding Information: * Corresponding author. E-mail: [email protected]. {\textquoteright} Supported in part by NSF grant DMS-9203981 and the Center for Communication University of Nebraska - Lincoln.",

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AU - Trotter, P. G.

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Algorithmic problems for finite groups and finite 0-simple semigroups

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