Namespaces
Variants
Actions

Difference between revisions of "Talk:Sporadic simple group"

From Encyclopedia of Mathematics
Jump to: navigation, search
(table rowspans)
(wikipediafs remarks, table formatting suggestion)
 
(9 intermediate revisions by 3 users not shown)
Line 1: Line 1:
−
A [[Simple finite group|simple finite group]] that does not belong to any of the known infinite series of simple finite groups. The  twenty-six sporadic simple groups are listed in the following  table.
+
Post $\TeX$ remarks
 +
* I could not edit this page using my usual method (wikipediafs) so I could not fix the refs, could someone do it for me?
 +
* It might be nice to have some extra columns here
 +
** reference to the relevant paper
 +
** date of discovery
 +
** order in decimal
 +
* possibly allow sorting by some of these columns?
 +
I am seriously out of my depth on this topic, so I will leave it to others to consider whether these are worth doing ... -- [[User:Jjg|Jjg]] 21:12, 30 April 2012 (CEST)
  
−
{| class="wikitable"
+
: This math is out of my competence, but anyway I wonder, why wikipediafs failed here? --[[User:Boris Tsirelson|Boris Tsirelson]] 21:34, 30 April 2012 (CEST)
−
! notation
+
 
−
! name
+
:: Not sure, it may be a problem at my end, but now I cannot edit any pages via wikipediafs (even ones that I was editing yesterday). Very strange. --[[User:Jjg|Jjg]] 23:29, 30 April 2012 (CEST)
−
! order
+
 
−
|-
+
::: I don't know anything about wikipediafs, but its [http://en.wikipedia.or /wiki/WikipediaFS#Disadvantages wp page] says its version 0.3 does not work with current wp. I prefer working with browser extensions like "Edit with emacs" (chromium) and/or "It's all text" (firefox). --[[User:Ulf Rehmann|Ulf Rehmann]] 09:58, 1 May 2012 (CEST)
−
| $M_{11}$
+
 
−
| rowspan="5" | Mathieu groups
+
:::: The most recent version works fine, it has the disadvantage that it must login to make each each "commit", and does not give a lot of feedback when it fails (the above failure was due to the recent login problems), but at least it does work -- I spent a full evening trying to coerce "It's all text" to play nice, and I really don't want to change browser just to edit a page... --[[User:Jjg|Jjg]] 19:24, 2 May 2012 (CEST)
−
| $2^4.3^2.5.11$
+
 
−
|-
+
A lot of things could be added here. Each of the sporadic group names should have its own page. We only have the Mathieu groups as a distinguished page. --[[User:Ulf Rehmann|Ulf Rehmann]] 01:02, 1 May 2012 (CEST)
−
| $M_{12}$
+
 
−
| $2^6.3^3.5.11$
+
I like to propose that the word "group" be dropped from the second column and put in the header instead; eg
−
|-
+
$\newcommand{\d}{\cdot}$
−
| $M_{22}$
+
{| class="wikitable" style="margin: 1em auto 1em auto;"
−
| $2^7.3^2.5.7.11$
+
|+ The twenty-six sporadic simple groups
−
|-
+
! Notation
−
| $M_{23}$
+
! Name (group)
−
| $2^7.3^2.5.7.11.23$
+
! Order
−
|-
 
−
| $M_{24}$
 
−
| $2^{10}.3^3.5.7.11.23$
 
 
|-
 
|-
 
| $J_1$
 
| $J_1$
−
| Janko group
+
| Janko
−
| $2^3.3.5.7.11.19$
+
| $2^3\d 3\d 5\d 7\d 11\d 19$
−
|-
 
−
| $J_2$, $HJ$
 
−
| Hall–Janko group
 
−
| $2^7.3^3.5^2.7$
 
−
|-
 
−
| $J_3$, $HJM$
 
−
| Hall–Janko–McKay group
 
−
| $2^7.3^5.5.17.19$
 
−
|-
 
−
| $J_4$
 
−
| Janko group
 
−
| $2^{21}.3^3.5.7.11^3.23.29.31.37.43$
 
−
|-
 
−
| $Co_1$
 
−
| rowspan="3" | Conway groups
 
−
| $2^{21}.3^9.5^4.7^2.11.13.23$
 
−
|-
 
−
| $Co_2$
 
−
| $2^{18}.3^6.5^3.7.11.23$
 
−
|-
 
−
| $Co_3$
 
−
| $2^{10}.3^7.5^3.7.11.23$
 
−
|-
 
−
| $F_{22}$, $M(22)$
 
−
| rowspan="3" | Fischer groups
 
−
| $2^{17}.3^9.5^2.7.11.13$
 
−
|-
 
−
| $F_{23}$, $M(23)$
 
−
| $2^{18}.3^{13}.5^2.7.11.13.17.23$
 
−
|-
 
−
| $F_{24}^\prime$, $M(24)^\prime$
 
−
| $2^{21}.3^{16}.5^2.7^3.11.13.17.23.29$
 
−
|-
 
−
| $HS$
 
−
| Higman–Sims group
 
−
| $2^9.3^2.5^3.7.11$
 
−
|-
 
−
| $He$, $HHM$
 
−
| Held–Higman–McKay group
 
−
| $2^{10}.2^3.5^2.7^3.17$
 
−
|-
 
−
| $Suz$
 
−
| Suzuki group
 
−
| $2^{13}.3^7.5^2.7.11.13$
 
−
|-
 
−
| $M^c$
 
−
| McLaughlin group
 
−
| $2^7.3^6.5^3.7.11$
 
−
|-
 
−
| $Ly$
 
−
| Lyons group
 
−
| $2^8.3^7.5^6.7.11.31.37.67$
 
−
|-
 
−
| $Ru$
 
−
| Rudvalis group
 
−
| $2^{14}.3^3.5^3.7.13.29$
 
−
|-
 
−
| $O'N$, $O'NS$
 
−
| O'Nan–Sims group
 
−
| $2^9.3^4.5.7^3.11.19.31$
 
−
|-
 
−
| $F_1$, $M$
 
−
| Monster, Fischer–Griess group
 
−
| $2^{46}.3^{20}.5^9.7^6.11^2.13^3.17.19.23.29.31.41.47.59.71$
 
−
|-
 
−
| $F_2$, $B$
 
−
| Baby monster
 
−
| $2^{41}.3^{13}.5^6.7^2.11.13.17.19.23.31.47$
 
−
|-
 
−
| $F_3$, $E$, $Th$
 
−
| Thompson group
 
−
| $2^{15}.3^{10}.5^3.7^2.13.19.31$
 
 
|-
 
|-
−
| $F_5$, $D$, $HN$
 
−
| Harada–Norton group
 
−
| $2^{14}.3^6.5^6.7.11.19$
 
 
|}
 
|}
−
 
+
This is normal typographic practice in tables for units, for example.  It would have the advantage that it would free up some horizontal space for other columns, as suggested above. --[[User:Jjg|Jjg]] 19:24, 2 May 2012 (CEST)
−
====References====
 
−
<table><TR><TD  valign="top">[1]</TD> <TD valign="top">  S.A. Syskin,   "Abstract properties of the simple sporadic groups"  ''Russian Math.  Surveys'' , '''35''' :  5  (1980)  pp. 209–246  ''Uspekhi Mat. Nauk'' ,  '''35''' :  5  (1980)  pp. 181–212</TD></TR><TR><TD  valign="top">[2]</TD> <TD valign="top"> M. Aschbacher,    "The finite simple groups and their classification" , Yale Univ. Press  (1980)</TD></TR></table>
 
−
 
 
−
====Comments====
 
−
The  recent classification of the finite simple groups (1981) has led to the conclusion that — up to a uniqueness proof for the Monster as the only  simple group of its order with certain additional properties — every  non-Abelian finite simple group is isomorphic to: an [[Alternating  group|alternating group]] on at least 5 letters, a group of (twisted or untwisted) Lie type, or one of the above 26 sporadic groups. See [[#References|[a2]]] for a discussion of the proof.
 
−
 
 
−
====References====
 
−
<table><TR><TD  valign="top">[a1]</TD> <TD valign="top">  J.H. Conway,   R.T. Curtis,  S.P. Norton,  R.A. Parker,  R.A. Wilson,  "Atlas of  finite groups" , Clarendon Press  (1985)</TD></TR><TR><TD  valign="top">[a2]</TD> <TD valign="top">  D. Gorenstein,    "Finite simple groups. An introduction to their classification" ,  Plenum  (1982)</TD></TR></table>
 

Latest revision as of 17:24, 2 May 2012

Post $\TeX$ remarks

  • I could not edit this page using my usual method (wikipediafs) so I could not fix the refs, could someone do it for me?
  • It might be nice to have some extra columns here
    • reference to the relevant paper
    • date of discovery
    • order in decimal
  • possibly allow sorting by some of these columns?

I am seriously out of my depth on this topic, so I will leave it to others to consider whether these are worth doing ... -- Jjg 21:12, 30 April 2012 (CEST)

This math is out of my competence, but anyway I wonder, why wikipediafs failed here? --Boris Tsirelson 21:34, 30 April 2012 (CEST)
Not sure, it may be a problem at my end, but now I cannot edit any pages via wikipediafs (even ones that I was editing yesterday). Very strange. --Jjg 23:29, 30 April 2012 (CEST)
I don't know anything about wikipediafs, but its /wiki/WikipediaFS#Disadvantages wp page says its version 0.3 does not work with current wp. I prefer working with browser extensions like "Edit with emacs" (chromium) and/or "It's all text" (firefox). --Ulf Rehmann 09:58, 1 May 2012 (CEST)
The most recent version works fine, it has the disadvantage that it must login to make each each "commit", and does not give a lot of feedback when it fails (the above failure was due to the recent login problems), but at least it does work -- I spent a full evening trying to coerce "It's all text" to play nice, and I really don't want to change browser just to edit a page... --Jjg 19:24, 2 May 2012 (CEST)

A lot of things could be added here. Each of the sporadic group names should have its own page. We only have the Mathieu groups as a distinguished page. --Ulf Rehmann 01:02, 1 May 2012 (CEST)

I like to propose that the word "group" be dropped from the second column and put in the header instead; eg $\newcommand{\d}{\cdot}$

The twenty-six sporadic simple groups
Notation Name (group) Order
$J_1$ Janko $2^3\d 3\d 5\d 7\d 11\d 19$

This is normal typographic practice in tables for units, for example. It would have the advantage that it would free up some horizontal space for other columns, as suggested above. --Jjg 19:24, 2 May 2012 (CEST)

How to Cite This Entry:
Sporadic simple group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sporadic_simple_group&oldid=25778
Retrieved from "https://encyclopediaofmath.org/index.php?title=Talk:Sporadic_simple_group&oldid=25849"