Nilpotency and strong nilpotency for finite semigroups

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Almeida, J (Author) FCUP; Shahzamanian, MH (Author) FCUP; Kufleitner, M (Author) Other

Journal

Title: Quarterly Journal of Mathematics

Vol. 70

Pages: 619-648

ISSN: 0033-5606

Publisher: Oxford University Press

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00Q-WH3

DOI: 10.1093/qmath/hay059

Abstract (EN): Nilpotent semigroups in the sense of Mal'cev are defined by semigroup identities. Finite nilpotent semigroups constitute a pseudovariety, MN, which has finite rank. The semigroup identities that define nilpotent semigroups lead us to define strongly Mal'cev nilpotent semigroups. Finite strongly Mal'cev nilpotent semigroups constitute a non-finite rank pseudovariety, SMN. The pseudovariety SMN is strictly contained in the pseudovariety MN, but all finite nilpotent groups are in SMN. We show that the pseudovariety MN is the intersection of the pseudovariety BGnil with a pseudovariety defined by a kappa-identity. We further compare the pseudovarieties MN and SMN with the Mal'cev product J(m) G(nill).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 30