The number of nilpotent semigroups of degree 3.
type: Item
instance of: scholarly article
title: The number of nilpotent semigroups of degree 3.
zbMATH Open document ID: 1254.20049
author: Andreas Distler
author: J. D. Mitchell
published in: The Electronic Journal of Combinatorics
publication date: 2012-10-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.3529
full work available at URL: v19i2p51
review text: Summary: A semigroup is 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 on a set with \(n\in\mathbb N\) elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups on a set with \(n\) elements up to equality and up to isomorphism.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 20-04
zbMATH DE Number: 6098338
zbMATH Keywords: finite semigroups
zbMATH Keywords: nilpotent semigroups
zbMATH Keywords: numbers of semigroups
zbMATH Keywords: power group enumeration
zbMATH Keywords: nilpotency degrees
describes a project that uses: GAP
describes a project that uses: Smallsemi
MaRDI profile type: Publication
arXiv ID: 1201.3529
description: scientific article; zbMATH DE number 6098338