Reduction theorem for the type-II conjecture for finite monoids
\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)].\}
scientific article; zbMATH DE number 4204661
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