Comments on: more iguanodons via kfarey.sage

By: Farey symbols of sporadic groups | neverendingbooks

Farey symbols of sporadic groups | neverendingbooks — Tue, 07 Dec 2010 13:10:56 +0000

[...] groups turned out to be part of a (conjecturally) infinite sequence of simple groups, starting as follows [...]

By: Pages tagged "iguanodon"

Pages tagged "iguanodon" — Sat, 12 Jan 2008 19:21:28 +0000

[...] online community. The best part is … it’s all 100% free! Check them out here: Join Hey Nielsen! more iguanodons via kfarey.sage saved by 1 others LouRyder bookmarked on 01/12/08 | [...]

By: Josh

Josh — Mon, 17 Dec 2007 01:53:28 +0000

I looked in the ATLAS, and for some of the simple groups the dimension of the smallest nontrivial permutation representation is huge.

FYI: I also found a reference (R. A. Wilson, Standard generators for the sporadic simple groups, J. Algebra 184 (1996) 505-515.) that says that all the sporadics can be generated by an element of order 2 and an element of order 3, except M{11}, M{22}, M_{23}, and McL (A. J. Woldar, On Hurwitz generation and genus actions of sporadic groups, Illinois J. Math. 33 (1989) 416-437).

By: lieven

lieven — Tue, 11 Dec 2007 19:02:59 +0000

Here is the little I know about standard generators for the sporadics

But one also needs a permutation representation of moderate dimension, so the next testcase is J2 with its 100-dml permutation rep. Ive done some preliminary calculations and may post on it later.

By: Josh

Josh — Tue, 11 Dec 2007 18:30:16 +0000

Is every sporadic finite simple group a quotient of PSL_2(Z)?

I seem to recall reading the result that every finite simple group can be generated by two elements. Since PSL_2(Z) is isomorphic to the free product of Z/2 and Z/3, I wonder if every sporadic finite simple group can be generated by an element of order 2 and an element of order 3? (The result seems a bit unlikely for all finite simple groups, but maybe it holds for the sporadic ones and for one of the infinite families?)