Names of The Sporadic Groups
Five of the sporadic groups were discovered by Mathieu in the 1860s and the other 21 were found between 1965 and 1975. Several of these groups were predicted to exist before they were constructed. Most of the groups are named after the mathematician(s) who first predicted their existence. The full list is:
- Mathieu groups M11, M12, M22, M23, M24
- Janko groups J1, J2 or HJ, J3 or HJM, J4
- Conway groups Co1 or F2−, Co2, Co3
- Fischer groups Fi22, Fi23, Fi24′ or F3+
- Higman–Sims group HS
- McLaughlin group McL
- Held group He or F7+ or F7
- Rudvalis group Ru
- Suzuki sporadic group Suz or F3−
- O'Nan group O'N
- Harada–Norton group HN or F5+ or F5
- Lyons group Ly
- Tits group T
- Thompson group Th or F3|3 or F3
- Baby Monster group B or F2+ or F2
- Fischer–Griess Monster group M or F1
Matrix representations over finite fields for all the sporadic groups have been constructed.
The earliest use of the term "sporadic group" may be Burnside (1911, p. 504, note N) where he comments about the Mathieu groups: "These apparently sporadic simple groups would probably repay a closer examination than they have yet received".
Diagram is based on diagram given in Ronan (2006). The sporadic groups also have a lot of subgroups which are not sporadic but these are not shown on the diagram because they are too numerous.
Read more about this topic: Sporadic Group
Famous quotes containing the words names of, names and/or groups:
“The names of all fine authors are fictitious ones, far more so than that of Junius,—simply standing, as they do, for the mystical, ever-eluding Spirit of all Beauty, which ubiquitously possesses men of genius.”
—Herman Melville (1819–1891)
“And even my sense of identity was wrapped in a namelessness often hard to penetrate, as we have just seen I think. And so on for all the other things which made merry with my senses. Yes, even then, when already all was fading, waves and particles, there could be no things but nameless things, no names but thingless names. I say that now, but after all what do I know now about then, now when the icy words hail down upon me, the icy meanings, and the world dies too, foully named.”
—Samuel Beckett (1906–1989)
“... until both employers’ and workers’ groups assume responsibility for chastising their own recalcitrant children, they can vainly bay the moon about “ignorant” and “unfair” public criticism. Moreover, their failure to impose voluntarily upon their own groups codes of decency and honor will result in more and more necessity for government control.”
—Mary Barnett Gilson (1877–?)