The Lattice of image-Classes of (image, σ)-Irreducible Monoids Original Research Article

In this paper, we introduce a new concept, namely, the (image, σ)-irreducible monoid. LetG0be a simple algebraic group. Let σ be a surjective endomorphism ofG0such that (G0)σ, the fixed points ofG0under σ, is finite. We construct a (image, σ)-irreducible monoidMwithGthe unit group. Extending σ toM, we obtain a finite monoidMσwhich is image-irreducible. IfMis image-irreducible, we give a precise recipe to determine the lattices of image-classes ofMandMσ.