> < ^ Date: Fri, 21 Jan 2000 18:53:52 +0100
> < ^ From: Stefan Kohl <kohl@mathematik.uni-stuttgart.de >
> < ^ Subject: Re: generators and L_2

Dear GAP-Forum,

Scott Moser wrote:

I am trying to represent and view the projectivve specail linear group
(for example, L_2(13) ). One can easily construct the group using GAP's
SL(2,13) special linear group command in conjunction with the FactorGroup
command.

However... when i ask GAP to list the generators of the group, it produces
two group elements: one of order 6 and one of order 3. I wish to express
the group with two generators, one of order 2 and one of order 7. I am
certain this can be done ('the atlas of finite groups' asserts the
gereators existance, buuut not their form), but am unable to get GAP to
help me to this end - any suggestions??

Well, if I did not missunderstand you, this can be done easily :

```gap> G := PSL(2,13);     # Let G := L_2(13)
Group([ ( 3,13,11, 9, 7, 5)( 4,14,12,10, 8, 6),
( 1, 2, 9)( 3, 8,10)( 4, 5,12)( 6,13,14) ])
gap> Size(G);
1092
gap> g1 := First(AsList(G), g -> Order(g) = 2);
( 3, 9)( 4,10)( 5,11)( 6,12)( 7,13)( 8,14)
gap> g2 := First(AsList(G), g -> Order(g) = 7);
( 1, 2, 3, 5, 8,11,13)( 4,10, 7,14, 9, 6,12)
gap> H := Group(g1,g2);  # Just try it ...
Group([ ( 3, 9)( 4,10)( 5,11)( 6,12)( 7,13)( 8,14),
( 1, 2, 3, 5, 8,11,13)( 4,10, 7,14, 9, 6,12) ])
gap> Size(H);
1092                     # ... g1 and g2 generate the
# whole group, this is what you want.
```

Hope this helps,

Stefan

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