Let s be the full transformation semigroup on 4 elements:
t:=Transformation([1,2,3,3]);; s:=Semigroup(Transformation([2,1,3,4]),Transformation([2,3,4,1]),t);; Now we ask GAP to give us the Rees Zero Matrix Semigroup associated to the D-class of t: gap> ld:=GreensDClassOfElement(s,t);; gap> rs:=AssociatedReesMatrixSemigroupOfDClass(ld); Rees Zero Matrix Semigroup over Monoid( [ (1,2)(3,4)(5,6), (), (1,5,4)(2,3,6), (1,6)(2,4)(3,5), (1,3)(2,5)(4,6), (1,4,5)(2,6,3), 0 ], ... ) Since the semigroup s is regular, every D-class is regular and hence there exists at least one non-zero entry in each row and in each column in the Sandwich Matrix of rs. However, when we ask GAP to give the associated matrix we get: gap> SandwichMatrixOfReesZeroMatrixSemigroup(rs); [ [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ] ] If this was correct, then, in particular, the D-class of t would have no idempotents (and hence t would be irregular). I would be very grateful if someone could tell me what I am doing wrong. Joao _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
