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Anyone familiar with "GAP" for group arithemetic?

  1. Sep 19, 2015 #1
    Hi guys,

    There is a software package called GAP for "Groups, Algorithms, and Programming" with emphasis on Group Theory. You can download it for free. I did. However I'm finding it so intractable to use. I would like to find the "missing group" in the Symmetric groups. That is, the group order which divides the size of ##S_n## but is not a subgroup of ##S_n##. I'm sure GAP can do it. So far I got the following code down:

    (* first just get the group *)
    mygroup:=SymmetricGroup(4);
    subgroups:=AllSubgroups(mygroup);

    and that's about as far as I can go with it for now. At this point "subgroups" contain all the subgroups of mygroup. I would like then to create a table of group size, total subgroups, then I can find the missing ones.

    Anyone here familiar with using GAP can help me with this?

    Thanks,
    Jack
     
  2. jcsd
  3. Sep 24, 2015 #2
  4. Sep 24, 2015 #3
    Hi Greg,

    I'm making progress with the code. I had started another thread pertaining to the data from GAP where I posted a brilliant piece of GAP code I painfully pieced together:

    https://www.physicsforums.com/threads/converse-of-lagranges-theorem-for-groups.833243/

    I contacted their support as you suggested for another project I'm working on this time pertaining to conjugate classes in the symmetric groups. Thanks,

    Jack
     
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