On Wed, 14 Dec 2011, Luyện Lê Văn wrote:
When I ran the below code lines:
gap >S:=SymmetricGroup(3);;
gap >G:=DirectProduct(S);;
gap >G=S;
true
gap >C:=CyclicGroup(3);;
gap >G:=DirectProduct(C);;
gap >G=C;
false
The issue is that "equal" and "isomorphic" are not the same thing for
groups (among other structures). In fact in GAP there is also the
notion of "identical", but that doesn't apply to your example.
So identical==>equal==>isomorphic, but the converses are false.
For your example:
gap> S:=SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> G:=DirectProduct(S);
Group([ (1,2,3), (1,2) ])
gap> G=S;
true
gap> IsomorphismGroups(G,S);
[ (1,2,3), (1,2) ] -> [ (1,2,3), (1,2) ]
gap> C:=CyclicGroup(3);
<pc group of size 3 with 1 generators>
gap> G:=DirectProduct(C);
<pc group of size 3 with 1 generators>
gap> G=C;
false
gap> IsomorphismGroups(G,C);
[ f1 ] -> [ f1 ]
gap> S=C;
false
gap> IsomorphismGroups(S,C);
fail
--mike
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
