Idempotents, regular elements and sequences from finite semigroups
type: Item
instance of: scholarly article
title: Idempotents, regular elements and sequences from finite semigroups
zbMATH Open document ID: 0871.20051
DOI: 10.1016/0012-365X(95)00223-J
author: O. Diekmann
published in: Discrete Mathematics
publication date: 1997-10-06T00:00:00Z
review text: The paper proves a combinatorial result, the likes of which have proved useful in finite semigroup theory, that if \(n\) is the number of non-idempotent elements of a finite semigroup \(S\) then any product of length \(2^n\) has an idempotent factor (regarding the product as a word). The proof is a straightforward induction argument and examples which exploit properties of Zimin words show the bound of \(2^n\) is best possible. From this they calculate explicitly the integer \(b(n)\) such that for every semigroup of \(n\) elements any product of length \(b(n)\) has an idempotent factor. The value of \(b(n)\) is of the order of \(4^{n/3}\), the precise value depends on \(n\pmod 3\). The proofs allow similar results to be derived for other semigroup classes and element types.
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 1018480
zbMATH Keywords: regular elements
zbMATH Keywords: numbers of nonidempotent elements
zbMATH Keywords: finite semigroups
zbMATH Keywords: idempotent factors
zbMATH Keywords: Zimin words
MaRDI profile type: Publication
cites work: Q3772420
cites work: Q5564342
cites work: Biordered Sets of Eventually Regular Semigroups
cites work: On Finite Semigroups and Idempotents
cites work: On regular semigroups
cites work: Epimorphisms, permutation identities and finite semigroups
cites work: ALGORITHMIC PROBLEMS IN VARIETIES
cites work: Q3341054
full work available at URL: 0012-365x(95)00223-j
OpenAlex ID: W2000014440
description: scientific article; zbMATH DE number 1018480