Thanks, John. Mathworld and a couple of other lists I like to consult didn't have this. And Conrad says the "quaternion group" is the dicyclic group of order 8, the smallest member of this infinite family of nonabelian groups of order 4m. Also known as "binary dihedral." So maybe I'll just implement the whole family, and possibly the construction will build the KleinFourGroup for m=1.
Rob On Oct 16, 7:49 pm, John H Palmieri <jhpalmier...@gmail.com> wrote: > On Oct 16, 6:26 pm, Rob Beezer <goo...@beezer.cotse.net> wrote: > > > In introductory group theory, I like to be sure to expose the students > > to every group of order 15 or less. As permutation groups, most of > > these are easily available in Sage via cyclic permutation groups, > > perhaps along with the function that builds direct products, dihedral > > groups, etc. There are two gaps to fill though. Trac #7151 adds the > > "quaternion group" (nonabelian, order 8). The remaining group is the > > semidirect product of Z_3 by Z_4 (one presentation is <s, t; s^6 = 1, > > s^3 = t^2, sts = t>). > > > The nonabelian group of order 4 is known in Sage as the > > "KleinFourGroup". > > > My question: anybody know a succinct name for the above group of order > > 12? I've seen it listed a few places as "T" - does that have a > > history? > > Wikipedia seems to call it a "dicyclic group": see > > <http://en.wikipedia.org/wiki/List_of_small_groups> > <http://en.wikipedia.org/wiki/Dicyclic_group> > > The same name is given in > > <http://www.math.uconn.edu/~kconrad/blurbs/grouptheory/group12.pdf> > > and kconrad does not seem to have written the wikipedia page, so there > are two independent sources. > > John --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
