Reduction theorem for the type-II conjecture for finite monoids
type: Item
instance of: scholarly article
title: Reduction theorem for the type-II conjecture for finite monoids
zbMATH Open document ID: 0729.20026
DOI: 10.1016/0022-4049(90)90048-M
author: Karsten Henckell
author: John L. Rhodes
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: \textit{J. Rhodes} and \textit{B. Tilson} [J. Pure Appl. Algebra 2, 13-71 (1972; Zbl 0257.20059)] introduced the notion of Type II elements in a finite monoid, showing that in the regular case these elements form the smallest submonoid that admits ``conjugation''. In doing so, they confirmed for finite regular monoids what has become known as the Type II conjecture. The present paper advances the general study of the Type II conjecture by showing that it can be reduced to the case of block groups, monoids in which every element has at most one inverse. Using this reduction procedure, the authors are able to prove certain special cases of the Type II conjecture, and to simplify existing proofs of some special cases. \{Reviewer's remark: the type II conjecture is now a theorem, having been verified in the general case by \textit{C. J. Ash} [Semigroup Theory, Proc. Monash Univ. Conf. Semigroup Theory in Honour of G. B. Preston, eds. T. E. Hall, J. C. Meakin and P. R. Jones (World Scientific, Singapore) (1991)].\}
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 4204661
zbMATH Keywords: finite regular monoids
zbMATH Keywords: Type II conjecture
zbMATH Keywords: block groups
Wikidata QID: Q122965850
reviewed by: Graham T. Clarke
MaRDI profile type: Publication
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full work available at URL: 0022-4049(90)90048-m
OpenAlex ID: W2018994876
description: scientific article; zbMATH DE number 4204661