Talk:Mathieu group

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[edit] Constructions

The constructions of M12 and M24 that I have described may have been Mathieu's original constructions, but I have not had access to his papers. Scott Tillinghast, Houston TX 03:17, 7 June 2007 (UTC) The oldest reference I have actually seen is Carmichael's book. He does not attribute the generators to anyone. Scott Tillinghast, Houston TX 05:15, 27 June 2007 (UTC)

[edit] Internal links

I am thinking about making some internal links in this article. Some of the maximal subgroups listed at the end are relevant in earlier sections Scott Tillinghast, Houston TX (talk) 05:01, 5 May 2008 (UTC)

[edit] Language problem

This article is written at a level that only advanced mathematicians can understand. At the very least, the article needs an introduction that is more easily understood by a general audience. Dr. Submillimeter 10:41, 30 March 2007 (UTC)

Introductory section has been revised. Scott Tillinghast, Houston TX (talk) 14:00, 24 March 2008 (UTC)

[edit] Summary of sources, aids to editors

It has been requested of me to summarize the sources of where I get the material, as an aid to others who want to edit.

[edit] Automorphism groups of Steiner systems

This comes mostly from Dixon and Mortimer's Permutation Groups. The development is bottom-up: start with the quaternion group and PSL(3,4) (also called M21) as nest eggs and work upward.

[edit] Automorphism group of the Golay code

From Thomas Thompson's Carus monograph (especially appendix) and Robert Griess's Twelve Sporadic Groups (chapter 5).

[edit] Sextet subgroup

This comes from Robert Griess's Twelve Sporadic Groups, chapter 4. His treatment is quite sophisticated, so I worked out my own presentation.

I found I could make a link to the hexacode.

I was considerably exposed to a socratic way of teaching, so I have left you, dear readers, with a set of generators and you can play around with the sextet group as you like.

For the points I used alphabetic characters. They have nothing to do with the alphanumeric characters I used in an earlier section to describe generating permutations.

[edit] Maximal subgroups

Robert Griess in chapter 6 describes the maximal subgroups of M24 and refers to the 1977 paper of Robert T. Curtis.

Conway and Sloane list on one page the maximal subgroups of all 5 Mathieu groups.

Then there are the ATLAS webites of Robert A. Wilson et al. They list all the maximal subgroups of Mathieu groups.

You may wonder why I have omitted maximal subgroups of M12 and M11. I have worked on text but I am in a quandary and want to think about it. I started on Mathieu groups with M11 and worked bottom-up, and liked doing it that way. The listing of maximal subgroups is top-down. So I am not sure what comments to make about subgroups of M11 and M12. M11 has permutation representations of degrees both 11 and 12!

Scott Tillinghast, Houston TX (talk) 04:56, 5 May 2008 (UTC)


[edit] Multiply transitive phrasing

I didn't like this phrase: It follows from the classification of finite simple groups that the only groups which are k-transitive for k at least 4 are the symmetric and alternating groups (of degree k and k-2 respectively)

This is easily misunderstood: A hurried reader may read this as an assertion that the alternating group Ak-2 is k-transitive.

Suggested rephrasing: It follows from the classification of finite simple groups that the only groups which are k-transitive for k at least 4 are the symmetric groups Sk and the alternating groups Ak+2

Cool dude ragnar (talk) 06:57, 18 May 2008 (UTC)

Sounds good. JackSchmidt (talk) 00:28, 19 May 2008 (UTC)