Opened 11 years ago

Closed 5 years ago

## #12073 closed defect (wontfix)

# MatrixGroup() or order() incorrect for G_2(F_3)

Reported by: | Robert Harron | Owned by: | joyner |
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Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |

Component: | group theory | Keywords: | MatrixGroup, GAP, order |

Cc: | Merged in: | ||

Authors: | Reviewers: | Travis Scrimshaw | |

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

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: M = MatrixGroup(gens); M.order() 8491392 sage: M.gap().Size() 8491392 sage: M.gap().Order() 8491392 sage: gap.Group([gap(gens[0]),gap(gens[1])]).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

### Change History (14)

### comment:1 Changed 9 years ago by

Milestone: | sage-5.11 → sage-5.12 |
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### comment:2 Changed 9 years ago by

Milestone: | sage-6.1 → sage-6.2 |
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### comment:3 Changed 9 years ago by

Milestone: | sage-6.2 → sage-6.3 |
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### comment:4 Changed 8 years ago by

Milestone: | sage-6.3 → sage-6.4 |
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### comment:5 Changed 7 years ago by

Stopgaps: | → todo |
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### comment:6 Changed 6 years ago by

Description: | modified (diff) |
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### comment:7 Changed 6 years ago by

Description: | modified (diff) |
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### comment:8 Changed 6 years ago by

Description: | modified (diff) |
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### comment:9 Changed 6 years ago by

### comment:10 Changed 6 years ago by

same problems for other finite fields of prime order

sage: p=5; L = [gap(GF(p)(i)) for i in range(p)]; L [0*Z(5), Z(5)^0, Z(5), Z(5)^3, Z(5)^2]

versus

gap> p:=5; [0..p-1]*Z(p); 5 [ 0*Z(5), Z(5), Z(5)^2, Z(5)^0, Z(5)^3 ]

**EDIT**
Note also that

gap> One(ZmodnZ(5)); Z(5)^0 gap> One(Z(5)); Z(5)^0 gap> One(GF(5)); Z(5)^0

So our conversion seems to be consistent with gap..

### comment:11 Changed 6 years ago by

This boils down to

gap> 1*Z(5); Z(5) gap> One(Z(5)); Z(5)^0

which is indeed not very-good looking.

### comment:12 Changed 6 years ago by

Milestone: | sage-6.4 → sage-duplicate/invalid/wontfix |
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Status: | new → needs_review |

Stopgaps: | todo |

ok, so this must come from a confusion: in Gap, Z(5) is not the one of the finite field, but a generator of the group of invertible elements. This means that your matrices are not the correct ones, I think.

I propose to close this as invalid.

### comment:13 Changed 6 years ago by

Reviewers: | → Travis Scrimshaw |
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Status: | needs_review → positive_review |

Confirmed:

gap> One(GF(5)); Z(5)^0

and replacing by the above yields:

gap> Order(Group( m1, m2 )); 8491392

From the GAP manual:

The root returned by

`Z`

is a generator of the multiplicative group of the finite field with p^{d}elements, which is cyclic.

### comment:14 Changed 5 years ago by

Resolution: | → wontfix |
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Status: | positive_review → closed |

Closing tickets in the sage-duplicate/invalid/wontfix module with positive_review (i.e. someone has confirmed they should be closed).

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