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Dear GAP Forum,

Mario Pineda Ruelas asked:

I am working with GAP 3.4.4 version for mac PPC. The groups that I am

investigating are transitives, imprimitives and are contained in S_12.

However now the size of some of this groups gives to me problems. Forexample:

gap> g:=Group((1,2)(3,4),(1,3,5)(2,4,6),(3,5,7,9,11)(4,6,8,10,12)); Group( (1,2)(3,4), (1,3,5)(2,4,6), ( 3, 5, 7, 9,11)( 4, 6, 8,10,12) ) gap> Size(g); 11520 gap> lat:=Lattice(g); Error, sorry, can' t identify the group's solvable residuum in

You have reached the limits of the capabilities of GAP 3 as documented in

the manual.

The subgroup lattice program in GAP 3 is only guaranteed to work if the

groups solvable residuum is not larger than 5000. (The algorithm uses a data

base of recomputed information and this information is not available for

larger groups). Your group <g> is perfect an thus equal to its solvable

residuum, so there is no easy way to compute the subgroup lattice.

The only way around this problem would be to provide the pwerfect subgroups

a priori from theory.

The manual secion on `Lattice' gives an example on how to do this.

The subgroup lattice function in GAP 4 has been improved and will work for

much larger groups (and -- provided memory being available -- should work

for all subgroups of S12).

However the code is quite different and thus it is not possible to make this

available for GAP 3.

If I have the generators of the group ? how to request to GAP subgroups

of certain size.

Unless the subgroups are of prime power order the only general algorithm I

am aware of would be to use the subgroup lattice, so there is no way around

this problem in GAP 3.

Best regards,

Alexander Hulpke

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