## Not all the semigroups <AGL(1,7), a>\AGL(1,7) are idempotent generated.
##
## GAP log file

gap> n:=7;; G:=PrimitiveGroup(7,4);; a:=Transformation( [ 1, 2, 3, 3, 3, 3, 3 ] );;
gap> gens:=List(GeneratorsOfGroup(G), x-> AsTransformation(x, n));;
gap> S:=Semigroup(Concatenation(gens, [a]));;
gap> Size(S);
2989
gap> I:=Idempotents(S, 3);;
gap> T:=Semigroup(I);
<semigroup with 42 generators>
gap> Size(T)=Size(S)-Size(G);
false