[sage-support] Re: Generating all subgroups of a group

2008-09-24 Thread Rob Beezer
Carlo and John, Thanks for the replies - those are both very helpful, and exactly the sort of thing I was hoping to learn about. It appears to me that H.normalizer() expects just a single element as an argument (rather than a whole subgroup), and returns a Group (rather than a PermutationGrou

[sage-support] Re: Generating all subgroups of a group

2008-09-24 Thread John Cremona
In Rob's example it would be nice (and good for the students to see) if instead of looping over all g in G to construct conjugate subgroups he could loop over coset representatives of H in G (where H is his representative_subgroup), or (optimal) coset reps of the normalizer of H in G. Now we can

[sage-support] Re: Generating all subgroups of a group

2008-09-24 Thread David Joyner
On Wed, Sep 24, 2008 at 2:05 PM, Carlo Hamalainen <[EMAIL PROTECTED]> wrote: > > On Wed, Sep 24, 2008 at 7:29 PM, Rob Beezer <[EMAIL PROTECTED]> wrote: >> >> A homework exercise for my students asks them to find all subgroups of >> S_4, which should be a very instructive exercise, even if a bit >>

[sage-support] Re: Generating all subgroups of a group

2008-09-24 Thread Carlo Hamalainen
On Wed, Sep 24, 2008 at 7:29 PM, Rob Beezer <[EMAIL PROTECTED]> wrote: > > A homework exercise for my students asks them to find all subgroups of > S_4, which should be a very instructive exercise, even if a bit > unreasonable. In SAGE, the conjugacy_classes_subgroups() method > gets you starte