4.14 Display a Transformation Monoid

Display( M )

Display displays the Green class structure of the transformation monoid M. Each D class is displayed as its index in the list of all D classes followed by some information about its structure in parenthesis. A D class displayed as

[a.b.d]

is a regular D class with a Schaccent127utzenberger group of size a, consisting of b L classes, or d R classes. A D class displayed as

{a.bxc.dxe}

is a nonregular D class with a Schaccent127utzenberger group of size a, consisting of <b> x <c> L classes (of which c have the same kernel), or <d> x <e> R classes (of which e have the same image).

    gap> M:= Monoid( Transformation( [ 7, 7, 1, 1, 5, 6, 5, 5 ] ), 
    > Transformation( [ 3, 8, 3, 7, 4, 6, 4, 5 ] ) );;
    gap> Size( M );
    27
    gap> Display( M );
    Rank 8: 1[1.1.1] 
    Rank 6: 3{1.1x1.1x1} 
    Rank 5: 6{1.1x1.1x1} 
    Rank 4: 2{1.1x1.1x1} 8[2.1.1] 
    Rank 3: 4{1.1x1.4x1} 5[1.3.4] 
    Rank 2: 7[1.5.1] 

The partial order of D classes (see PartialOrderDClasses) is determined in terms of the indices that serve as names of D classes for Display.

    gap> HasseDiagram(PartialOrderDClasses(M));
    Relation( [ [ 2, 3 ], [ 5 ], [ 6 ], [ 7 ], [ 4 ], [ 8 ], [  ], 
    [ 5 ] ] ) 

   
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