#12073: MatrixGroup() or order() incorrect for G_2(F_3)
----------------------------+-----------------------------------------------
Reporter: robharron | Owner: joyner
Type: defect | Status: new
Priority: major | Milestone: sage-4.8
Component: group theory | Keywords: MatrixGroup, GAP, order
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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If I use the generators for the exceptional group G_2(F_3) in its natural
7-dimensional representation over F_3 in the MatrixGroup constructor, the
order of the group returned is 8491392 (twice what it should be). However,
if I use the same generators through the gap console within sage, I get
the correct size.
{{{
K=GF(3)
sage: gens=[matrix(K,7,[
....: [0,2,0,0,0,0,0],
....: [2,0,0,0,0,0,0],
....: [0,0,0,2,0,0,0],
....: [0,0,2,0,0,0,0],
....: [0,0,0,0,0,2,0],
....: [0,0,0,0,2,0,0],
....: [2,2,2,2,1,1,1]]),
....: matrix(K,7,[
....: [2,0,0,0,0,0,0],
....: [0,0,2,0,0,0,0],
....: [1,1,1,0,0,0,0],
....: [0,0,0,0,2,0,0],
....: [1,0,0,1,1,0,0],
....: [0,0,0,0,0,0,2],
....: [1,0,0,0,0,1,1]])]
sage: MatrixGroup(gens).order()
8491392
}}}
{{{
gap> m1:= [
> [0,2,0,0,0,0,0],
> [2,0,0,0,0,0,0],
> [0,0,0,2,0,0,0],
> [0,0,2,0,0,0,0],
> [0,0,0,0,0,2,0],
> [0,0,0,0,2,0,0],
> [2,2,2,2,1,1,1]
> ]*Z(3);
gap> m2:= [
> [2,0,0,0,0,0,0],
> [0,0,2,0,0,0,0],
> [1,1,1,0,0,0,0],
> [0,0,0,0,2,0,0],
> [1,0,0,1,1,0,0],
> [0,0,0,0,0,0,2],
> [1,0,0,0,0,1,1]
> ]*Z(3);
gap> Order(Group( m1, m2 ));
4245696
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12073>
Sage <http://www.sagemath.org>
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