# 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 ] ) )
```

GAP 3.4.4
April 1997