Talk:Janko group

Would it be better to break this article up into four separate articles? Gene Ward Smith 22:01, 28 Oct 2004 (UTC)

These must be an error in the generators of the Hall-Janko group J2. You say (in effect) that w is a cube root of unity, and yet several components are listed as the cube of w. They would equal 1. Scott Tillinghast, Houston TX 1:27 PM 15 Jan 2006

The presentations (i. e. generators and relations) given are rather counterintuitive, and I wonder how much value they have in an introductory article.

There are interesting questions, however, about 2 cases with a of order 2, b of order 3, and ab of order 7. These relations alone define an infinite group, the symmetry group of a tiling of the hyperbolic plane. Assigning order 4 to the commutator [a,b] = ababb defines the simple group of order 168. J₁ can have [a,b] of order 19 or 11; J₂ can have [a,b] of order 12. I don't know whether more relations are needed to define J₁ and J₂ completely. I would be interested to see a classification of the groups defined by the first 3 relations.

I wonder how the matrix generators given for J₁ and J₂ are related to the presentations. Scott Tillinghast, Houston TX 21:34, 22 July 2006 (UTC)[reply]