A problem on central cryptogroups.
type: Item
instance of: scholarly article
title: A problem on central cryptogroups.
zbMATH Open document ID: 1114.20034
author: Guoxin Liu
author: Jiangang Zhang
published in: Semigroup Forum
publication date: 2007-01-26T00:00:00Z
review text: A completely regular semigroup \(S\) is called `central' if the product of any two idempotents of \(S\) lies in the center of the maximal subgroup containing it; if the Green relation \(\mathcal H\) is a congruence on \(S\), then \(S\) is called a `cryptogroup'. The classes of all cryptogroups, central cryptogroups and orthodox cryptogroups are denoted by \(\mathcal{BG}\), \(\mathcal{CBG}\) and \(\mathcal{OBG}\), respectively. A completely regular semigroup \(S\) is called `overabelian' if \(H_e\) are Abelian groups for all \(e\in E(S)\). \(\mathcal{BA}\) denotes the class of all overabelian cryptogroups. It is proved that \(\mathcal{OBG}\vee\mathcal{BA}=\mathcal{CBG}\).
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 5118906
zbMATH Keywords: varieties
zbMATH Keywords: central cryptogroups
zbMATH Keywords: orthodox cryptogroups
zbMATH Keywords: bands of Abelian groups
zbMATH Keywords: idempotents
reviewed by: Peeter Normak
MaRDI profile type: Publication
full work available at URL: s00233-006-0619-0
OpenAlex ID: W2008488810
DOI: 10.1007/S00233-006-0619-0
description: scientific article; zbMATH DE number 5118906