Talk:Conway group

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Contents 1 Versions of Robert A. Wilson website 2 Summary of sources, aids to editors 2.1 Opening of article 2.2 Other sporadic groups 2.3 The group 212:M24 2.4 Maximal subgroups of various subgroups

[edit] Versions of Robert A. Wilson website

I re-instated version 2 alongside version 3. The nice thing about version 2 is that lists of maximal subgroups have links to pages on the simple groups that are involved. Scott Tillinghast, Houston TX (talk) 21:45, 4 May 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. I would welcome suggestions about what else I should include.

[edit] Opening of article

I added in some history, which I mainly got from Thomas Thompson's Carus monograph. He talks about the groups he has space to give adequate mathematical treatment. That includes the 3 Conway groups and some basics about M₂₄, but he barely mentions the other 4 soradic groups of the second generation.

[edit] Other sporadic groups

The best source is Robert Griess's Twelve Sporadic Groups. Quite a bit of information, but there are many interesting questions he does not touch. He gives very little history on these groups.

For history I have resorted to the book edited by Brauer and Shih, a compilation of lectures from May 1968 conference at Harvard.

I am trying to enumerate all the conjugacy classes of simple subgroups and subquotients in Co₀, but this may constitute original research.

[edit] The group 2¹²:M₂₄

From Thomas Thompson. He relates how it began Conway's investigation, how he managed to prove this is a proper but maximal subgroup of Co₀. He could then deduce |Co₀|.

[edit] Maximal subgroups of various subgroups

Mainly from Robert A. Wilson's Atlas website. Perhaps it would be better to list the maximal subgroups of Co₀, but I don't know of a listing. The interesting thing about them is that some of them are direct products with maximal subgroups of Co₁, and others are stem extensions. It is Co₀ that is represented in SL(Q,24), as well as Co₂ and Co₃, but not Co₁.

Scott Tillinghast, Houston TX (talk) 04:05, 9 June 2008 (UTC)