On 15 March 2012 10:06, James Mitchell <j...@st-and.ac.uk> wrote: > Dear Shubh, > > The answer to your question is yes and no. There is *no* function in GAP > named IsRightFactorisableSemigroup, so in this sense the answer is no. On > the other hand, it should be more or less straightforward for a given > example of a semigroup to determine whether or not it is right factorisable > by examining its structure in GAP. If you have the Citrus package loaded, > then you can do the following: > > gap> gens:=[ Transformation( [ 2, 6, 7, 2, 6, 1, 1, 5 ] ), > > Transformation( [ 3, 8, 1, 4, 5, 6, 7, 1 ] ), > > Transformation( [ 4, 3, 2, 7, 7, 6, 6, 5 ] ), > > Transformation( [ 7, 1, 7, 4, 2, 5, 6, 3 ] ) ];; > gap> s:=Monoid(gens); > <monoid with 4 generators> > gap> GroupOfUnits(s); > Group(()) > gap> IsBand(s); > false > > which proves that this semigroup is not right factorisable. Another > example: > > gap> gens:=[Transformation([2,1,4,5,3,7,8,9,10,6]), > > Transformation([1,2,4,3,5,6,7,8,9,10]), > > Transformation([1,2,3,4,5,6,10,9,8,7]), > > Transformation([9,1,4,3,6,9,3,4,3,9])];; > gap> s:=Monoid(gens);; > gap> iter:=Iterator(s); > <iterator of transformation semigroup> > gap> g:=GroupOfUnits(s);; > gap> e:=Idempotents(s);; > gap> NrIdempotents(s); > 13655 > gap> t:=Set(Flat(List(e, x-> x*Elements(g))));; > gap> Length(t); > 186726 > gap> Size(s); > 491558 > > Which shows that the monoid <s> is also not right factorisable. > > I hope that that helps. > > Regards, > > James > > > From: "sh...@iitg.ernet.in" <sh...@iitg.ernet.in> > > Subject: [GAP Forum] Code for Right Factorisable Semigroup > > Date: 13 March 2012 11:13:51 GMT > > To: "fo...@gap-system.org" <fo...@gap-system.org> > > Cc: "forum-requ...@gap-system.org" <forum-requ...@gap-system.org> > > > > Dear Sir, > > Is there a code in GAP to check whether a semigroup is Right Factorisable > > or not. > > > > A semigroup S is right factorisable if S = EG for some subgroup G of S > and > > E is the set of all idempotents in S. > > > > > > > > With Regards, > > \-Shubh > -- > James Mitchell > tinyurl.com/jdmitchell > > The University of St Andrews is a charity registered in Scotland : No > SC013532 > > > > >
-- James Mitchell tinyurl.com/jdmitchell The University of St Andrews is a charity registered in Scotland : No SC013532 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
