Because it's not quite sporadic enough? The Tits group is *almost* a group of Lie type over a finite field -- see https://en.wikipedia.org/wiki/Ree_group for some context here. The group {}^2F_4(2^(2n+1)) is simple except for the case n=0, where you're looking at the group {}^2F_4(2) of order 2^12.3^3.5^2.13 -- that one turns out to have a subgroup of index 2, the Tits group. So you either lump the Tits group in with the of-Lie-type family, where you're only off by a factor of 2, or you lump it in with the 26 sporadic groups, where your count is only off by 1. --Michael On Fri, Oct 12, 2018 at 6:55 AM Colin Wright <math_fun@solipsys.co.uk> wrote:

Reading around for other things I came across this:

Re::// en.wikipedia.org/wiki/Classification_of_finite_simple_groups#Statement_of_the_classification_theorem

""" Theorem: Every finite simple group is isomorphic to one of the following groups:

* a member of one of three infinite classes of such, namely: * the cyclic groups of prime order, * the alternating groups of degree at least 5, * the groups of Lie type * one of 26 groups called the "sporadic groups" * the Tits group (which is sometimes considered a 27th sporadic group). """

So the Tits group is not one of the infinite families, and it's a finite simple group, so why isn't it fully and properly classed as one of the sporadic groups? What is a sporadic group if not just a finite simple group that's not one of the infinite families?

Colour me puzzled.

Colin -- Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different. -- Johann Wolfgang von Goethe 1749-1842

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

-- Forewarned is worth an octopus in the bush.