On Wed, Oct 21, 2009 at 1:35 AM, Rob Beezer <goo...@beezer.cotse.net> wrote: > > Hi David, > > Thanks for the comments. The "Quaternion Group" Wikipedia page seems > to differ substantially with the "Dicyclic Group" page: > > http://en.wikipedia.org/wiki/Dicyclic_group > > which says: > > "More generally, when n is a power of 2, the dicyclic group is > isomorphic to the generalized quaternion group." > > Its not obvious to me that presentation in the Quaternion page > guarantees that the group will have order 4n, as claimed there, but > perhaps that follows. If so, then as you have noted, it is identical > to what is called the dicyclic group on the other page. > > The docstring I have in the patch right now says: > 'When the order of the group is a power of 2 it is known as a > "generalized quaternion group." '
I think you are right and I am wrong. Most people in the literature say that a generalized quaternion group is a 2-group, so what you have doesn't need any change after all. The presentations are the same which I guess is what made me think they are the same. Sorry for the noise:-) > > If folks agree that the term "generalized quaternion group" just > applies when the order of the group is a power of 2, then I could make > a derived class for this, like I did for just the dicyclic group of > order 8, which I just call *the* quaternion group. I thought of doing > that, but it felt like overkill, and just went with comment in the > docstring. > > Thanks, > Rob > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
