62.25 IsSimple for semigroups

IsSimple( sg )

A semigroup S is called simple if it has no honest ideals, i.e. in case that S is finite the smallest ideal of S equals S itself.

The GAP standard library dispatcher function IsSimple calls the function sg.-op-er-a-tions.-Is-Simple which checks if the semigroup sg equals its smallest ideal and if so, returns true and otherwise false.

  gap> IsSimple( s );                                                    
  false
  gap> c3 := TransformationSemigroup( Transformation( [1..3],            
  >                                   [2,3,1] ) );
  TransformationSemigroup( Transformation( [ 1, 2, 3 ], [ 2, 3, 1 ] ) ) 
  gap> IsSimple( c3 );
  true

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