Talk:List of finite simple groups

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Untitled[edit]

Note that this page uses italic for group of Lie type A, but roman for the alternating groups.

If we are referring to groups of Lie type by their Dynkin diagrams (i.e. PSL(2,7) is A₁(7)), then it would be better not to call the alternating groups A_n. I've sometimes seen a Gothic A to make it clearer, and some authors use Alt_n. Otherwise people might think A_n(q) is related to A_n, which they're not. The difference between roman and italic is not enough to make it obvious imho. --Huppybanny 14:56, 18 October 2005 (UTC)[reply]

Unfortunately A_n is by far the most common notation for alternating groups, so it is probably best to stick to it. Using unusual notation like Alt_n may also confuse people used to the standard notation, and gothic letters probably dont work on all browsers. Maybe the best solution is to change it to boldface A_n. R.e.b. 16:11, 18 October 2005 (UTC)[reply]

"In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type (including the Tits group, which strictly speaking is not of Lie type), or one of 26 sporadic groups."

Surely the least comprehensible introductory sentence of all the articles in Wikipedia? —Preceding unsigned comment added by 24.222.128.60 (talk) 02:49, 27 February 2009 (UTC)[reply]

Yes, not easy to understand this first sentence. Also the fact that if you look in details their are 18 Lie groups and not 16. Or may be.. Don't you think classifying Z/Zp here is a bit too much, since it is the only "perfect" group and therefoe quite degenerated. Then move also the Tits groups into the sporadic category and indeed you have 16 families of Lie type ! --MD (talk) 06:45, 26 January 2010 (UTC)[reply]

Just wondered if there's any progress on a weighted factorization, i.e. why some apparent sporadic factors do not divide into the bigger sporadics. A simple stright factorization in this sense is a little misleading. —Preceding unsigned comment added by 217.171.129.69 (talk) 15:56, 9 August 2010 (UTC)[reply]

So if the 27 sporadics and 18 generics are a general product of a 2 and 3 radical system. (Is the height function of cubic root (a+b*cubert(-c))/d c equals one upto 22?)

The tits group (ab)^13 is the 12 real, not the 12+6 complex 18 cohomology sort of simplicity. Two of the pariah seem to be connected to the monster O'N (in the drawing note??), That leaves 4 absolute pariahs. Two which have sub group common factors, and 2 which don't. That umbral moonshine ... 188.29.164.90 (talk) 21:12, 6 October 2015 (UTC)[reply]

Or how about http://www.sciencedirect.com/science/article/pii/S0022314X06000217 and the 42 (= 18 + 26) cubic fields of class number 1. Interesting eh? So the 42 unique discriminants and the resultant polynomials characteristic of them. Currently I'm just counting the ones without some linear dependence of which I count 5, and I count 1 with no quadratic dependence. And 23 is the lowest. Curious ... 188.29.164.90 (talk) 00:02, 7 October 2015 (UTC)[reply]

Merge with the main page Classification_of_finite_simple_groups?[edit]

I don't think this should be on a separate page from Classification of finite simple groups since this is basically a more precise statement of that result. Also, the list is fixed, as per the theorem, and will not grow without bounds as other lists might. The information here would greatly complement that of the main page, especially the clear explanation of what the groups of Lie type are. Cirosantilli2 (talk) 12:34, 14 September 2021 (UTC)[reply]

False claims in the description of the automorphism groups[edit]

The paragraph describing the structure of the automorphism groups (just before the tables) contains false statements. For example: direct product of the groups of graph and field automorphisms does not form a complement to the group of inner diagonal automorphisms (within the group of all automorphisms). Cf. Gorenstein---Lyons-Solomon, Theorem 2.5.12.

Could someone please update that paragraph? I am a little shocked that such a big error remained on the page for so long ...

Mathsies (talk) 08:12, 25 February 2022 (UTC)[reply]