> < ^ From:

> < ^ Subject:

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

> < [top]