## File(s) not publicly available

# Algorithmic problems for finite groups and finite 0-simple semigroups

journal contribution

posted on 2023-05-16, 10:48 authored by Hall, TE, Kublanovskii, SI, Margolis, SW, Sapir, MV, Trotter, PGIt 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. Â© 1997 Published by Elsevier Science B.V.

## History

## Publication title

Journal of Pure and Applied Algebra## Volume

119## Pagination

75-96## ISSN

0022-4049## Department/School

School of Natural Sciences## Publisher

Elsevier Science Bv## Place of publication

Po Box 211, Amsterdam, Netherlands, 1000 Ae## Repository Status

- Restricted