Chapter 1. Extension of the fundamental theorem of finite semigroups

@article{Stiffler1973Chapter1E,
title={Chapter 1. Extension of the fundamental theorem of finite semigroups},
author={Price E. Stiffler},
journal={Advances in Mathematics},
year={1973},
volume={11},
pages={159-209}
}

ResumeAll semigroups considered are finite. The semigroup C is by definition combinatorial (or group free or aperiodic) iff the maximal subgroups of C are singletons. Let S2oS1 denote the wreath… Expand

Characterizing for any pseudovarieties of monoids U, V the smallest Pseudovariety W that contains U and such that W □ V = W allows us to obtain new decomposition results for a number of important varieties such as DA, DO and DA * G.Expand

It is shown that ZG is local, that is, the semidirect product ZG ∗ D of ZG by definite semigroups is equal to LZG, the variety of semig groups where all local monoids are in ZG.Expand

The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, Complexity of finite semigroups, Annals of Mathematics (2) 88 (1968),… Expand

Abstract We compute the quiver of any finite monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a… Expand

It is shown that any finite monoid S on which Green’s relations R and H coincide divides the monoid of all upper triangular row-monomial matrices over a finite group. The proof is constructive; given… Expand