The number of nilpotent semigroups of degree 3

Andreas Distler, James D. Mitchell

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree 3. We give formulae for the number of nilpotent semigroups of degree 3 with $n\in\N$ elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups with $n$ elements up to equality and up to isomorphism.
Original languageEnglish
Article numberP51
JournalElectronic Journal of Combinatorics
Volume19
Issue number2
Publication statusPublished - 2012

Fingerprint

Dive into the research topics of 'The number of nilpotent semigroups of degree 3'. Together they form a unique fingerprint.

Cite this