62.21 IdempotentElements for semigroups

IdempotentElements( sg )

An element i of a semigroup (S,cdot) is called an idempotent (element) if/f i cdot i = i.

The function IdempotentElements returns a list of those elements of the semigroup sg that are idempotent. (Note that for a finite semigroup this can never be the empty list).

  gap> IdempotentElements( s );
  [ Transformation( [ 1, 2, 3 ], [ 1, 1, 1 ] ), 
    Transformation( [ 1, 2, 3 ], [ 1, 2, 2 ] ), 
    Transformation( [ 1, 2, 3 ], [ 2, 2, 2 ] ), 
    Transformation( [ 1, 2, 3 ], [ 2, 2, 3 ] ), 
    Transformation( [ 1, 2, 3 ], [ 3, 3, 3 ] ) ]

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