62.15 TransformationSemigroup

TransformationSemigroup( t_1, ..., t_n )
TransformationSemigroup( [ t_1, ..., t_n ] )

When called in this form, the constructor function Trans-for-mation-Semi-group returns the transformation semigroup generated by the transformations t_1,~...,~t_n. There is another way to call this function:

TransformationSemigroup( n )

If the argument is a positive integer n, Trans-for-mation-Semi-group returns the semigroup of all transformations on the set {1,2, dots , n}.

  gap> t1 := Transformation( [1..3], [1,1,2] );
  Transformation( [ 1, 2, 3 ], [ 1, 1, 2 ] )
  gap> t2 := Transformation( [1..3], [2,3,3] );
  Transformation( [ 1, 2, 3 ], [ 2, 3, 3 ] )
  gap> s:=TransformationSemigroup( t1, t2 );
  TransformationSemigroup( Transformation( [ 1, 2, 3 ],
  [ 1, 1, 2 ], Transformation( [ 1, 2, 3 ], [ 2, 3, 3 ] ) )
  gap> s27 := TransformationSemigroup( 3 );
  TransformationSemigroup( Transformation( [ 1, 2, 3 ], 
  [ 1, 1, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 1, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 1, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 2, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 2, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 2, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 3, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 3, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 1, 3, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 1, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 1, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 1, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 2, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 2, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 2, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 3, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 3, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 2, 3, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 1, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 1, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 1, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 2, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 2, 2 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 2, 3 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 3, 1 ] ), Transformation( [ 1, 2, 3 ], 
  [ 3, 3, 2 ] ), Transformation( [ 1, 2, 3 ], [ 3, 3, 3 ] ) ) 

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