Dear GAP Forum,
In answer to Ignat Soroko's question: the elements g1 and g2 are not
invertible, if GF(3) in the example from the manual is replaced by
GF(2). A brute force way to see this is:
gap> Length(AsSet(List(AsList(rm),x->x*g1))); 16 gap> Size(rm); 256 gap> Length(AsSet(List(AsList(rm),x->x*g2))); 4
Regards,
Jan Draisma
In answer to > Dear GAP Forum, > > I was trying to execute example from the Reference Manual to GAP 4.2 > concerning group rings on page 567. For the field GF(3) all is OK, but > when I changed to GF(2) an error occured: > > gap> d8:=DihedralGroup(8); > <pc group of size 8 with 3 generators> > gap> rm:=FreeMagmaRing(GF(2),d8); > <algebra-with-one over GF(2), with 3 generators> > gap> emb:=Embedding(d8,rm); > <mapping: Group( [ f1, f2, f3 ] ) -> AlgebraWithOne( GF(2), ... ) > > gap> gens:=List(GeneratorsOfGroup(d8),x->x^emb); > [ (Z(2)^0)*f1, (Z(2)^0)*f2, (Z(2)^0)*f3 ] > gap> x1:=gens[1]+gens[2];; > gap> x2:=(gens[1]-gens[2])*gens[3];; > gap> x3:=gens[1]*gens[2]*(One(rm)-gens[3]);; > gap> g1:=x1-x2+x3;; > gap> g2:=x1+x2;; > gap> q8:=Group(g1,g2);; > Error usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) at > Error( "usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>)" ); > <function>( <arguments> ) called from read-eval-loop > Entering break read-eval-print loop, you can 'quit;' to quit to outer loop, > or you can return to continue > brk> > > The platform I'm working at is Windows 95, 98 (tested on both). > What can be done to remedy the situation? > > Sincerely yours, > > Ignat Soroko > e-mail: soroko@fpm.bsu.unibel.by >