[GAP Forum] Consults on GAP

[Hulpke,Alexander]

Dear Forum,

Jiayue asked:

> Em.. here is a question I have about GAP: 
> 
> Is there any operations like "AllSmallGroupsOfCharacterDegrees([...])"? 
> 
> How do we find the certain groups in GAP database(the SmallGroup Id will be fine)
> holding the given character degrees?


The operation `AllSmallGroups’ can select for groups satisfying certain functions, e.g the result of the function `CharacterDegrees’. For example, to get all groups of order 32 with 4 characters of degree  and 16 linear characters, one could use:

AllSmallGroups(Size,32,CharacterDegrees,[[[1,16],[2,4]]]);

(Note that, as the result is a list, we need to wrap it in a list once more to avoid GAP interpreting it as a collection of values, alternatively one could use it as:

AllSmallGroups(Size,32,x->CharacterDegrees(x)=[[1,16],[2,4]],true);

Note that the character degrees are not stored precomputed in the library, so GAP will have to compute them on the fly for all groups in the otherwise specified range. So doing this test for order 256 could take a long time.

If you do not care about multiplicities, you could take the degrees only with a small list operation, that is:

occurringDegrees:=g->List(CharacterDegrees(g),x->x[1]);
AllSmallGroups(Size,32,occurringDegrees,[[1,2]]);

would return the groups of order 32 with characters only of degree 1 and 2.

Regards,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke