#19594: Implement the cactus group
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: group theory | Resolution:
Keywords: cactus | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/groups/cactus_group-19594 | 7eb2a1278ea0ca08375f87e0f82081218a2ea1ec
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by dimpase):
There seems to be something wrong with the relations you provide.I am
trying to check that you indeed have a homomorphism from J_4 to Sym(4),
but GAP returns `fail`. Does your code check that your map is a group
homomorphism?
{{{
gap> F:=FreeGroup(6);
<free group on the generators [ f1, f2, f3, f4, f5, f6 ]>
gap> s12:=F.1;; s13:=F.2;; s14:=F.3;; s23:=F.4;; s24:=F.5;; s34:=F.6;;
gap> rels:=[s12^2, s13^2, s14^2, s23^2, s24^2, s34^2,
s13*s12*s13^-1*s23^-1, s13*s23*s13^-1*s12^-1, s14*s12*s14^-1*s34^-1,
s14*s13*s14^-1*s24^-1, s14*s23*s14^-1*s23^-1, s14*s24*s14^-1*s13^-1,
s14*s34*s14^-1*s12^-1, s24*s23*s24^-1*s34^-1, s24*s34*s24^-1*s23^-1,
s34*s12*s34^-1*s12^-1 ];
[ f1^2, f2^2, f3^2, f4^2, f5^2, f6^2, f2*f1*f2^-1*f4^-1,
f2*f4*f2^-1*f1^-1, f3*f1*f3^-1*f6^-1,
f3*f2*f3^-1*f5^-1, f3*f4*f3^-1*f4^-1, f3*f5*f3^-1*f2^-1,
f3*f6*f3^-1*f1^-1, f5*f4*f5^-1*f6^-1,
f5*f6*f5^-1*f4^-1, f6*f1*f6^-1*f1^-1 ]
gap> G:=F/rels;
<fp group on the generators [ f1, f2, f3, f4, f5, f6 ]>
gap> s4:=Group([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)]);
Group([ (1,2), (1,3), (1,4), (2,3), (2,4), (3,4) ])
gap> GeneratorsOfGroup(s4);
[ (1,2), (1,3), (1,4), (2,3), (2,4), (3,4) ]
gap> f:=GroupHomomorphismByImages(G,s4);
fail
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/19594#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
