eCite Digital Repository

Algorithmic problems for finite groups and finite 0-simple semigroups

Citation

Hall, TE and Kublanovskii, SI and Margolis, SW and Sapir, MV and Trotter, PG, Algorithmic problems for finite groups and finite 0-simple semigroups, Journal of Pure and Applied Algebra, 119, (1) pp. 75-96. ISSN 0022-4049 (1997) [Refereed Article]

DOI: doi:10.1016/S0022-4049(96)00050-3

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. © 1997 Published by Elsevier Science B.V.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Algebra and Number Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Hall, TE (Dr Hall)
Author:Margolis, SW (Professor Margolis)
Author:Sapir, MV (Professor Sapir)
Author:Trotter, PG (Dr Peter Trotter)
ID Code:11520
Year Published:1997
Web of Science® Times Cited:34
Deposited By:Mathematics
Deposited On:1997-08-01
Last Modified:2011-08-12
Downloads:0

Repository Staff Only: item control page