Talk:Conway group
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A question of clarity. Another contributor revised a sentence of mine concerning the relationship between the Happy Family and the Monster group. I will here sketch the relationship in more detail, and would welcome any suggestions on how to pare it down without losing clarity.
The Happy Family consists of 20 sporadic simple groups in 3 series, called generations:
1) The First Generation consists of the 5 Mathieu groups. The group M24 contains the other four.
2) The Second Generation consists of Conway 1 (Co1) and 6 proper subgroups. Co1 contains M24, but the 6 others do not. Some of the 6 contain smaller Mathieu groups.
3) The Third generation consists of the Monster and 7 proper subgroups. The Monster contains Co1, but the other 7 do not. I don't think the details about the Third Generation belong in this article.
THe Monster thus contains the other 19.
Scott Tillinghast, Houston TX 00:14, 6 February 2007 (UTC)
