The number of nilpotent semigroups of degree 3
Combinatorics
2012-08-23 v1 Rings and Algebras
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 elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups with elements up to equality and up to isomorphism.
Keywords
Cite
@article{arxiv.1201.3529,
title = {The number of nilpotent semigroups of degree 3},
author = {Andreas Distler and James D. Mitchell},
journal= {arXiv preprint arXiv:1201.3529},
year = {2012}
}