Wikipedia: History of Classification of finite simple groups

Difference (from prior major revision) (minor diff, author diff)

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A vast body of work, mostly published between around 1955 and 1983, classifies all of the finite simple groups. The classification shows all finite simple groups to be one of the following types:

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* an alternating groups of degree ≥ 5

* an alternating group of degree at least 5

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* an exceptional or twisted group of Lie type
* or one of 26 left over groups known as the sporadic groups

* an exceptional or twisted group of Lie type (including the Tits group)
* or one of 26 left-over groups known as the sporadic groups

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* McLaughlin? group McL?

* McLaughlin group McL

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The largest of the sporadic groups is the Monster group. It has 2⁴⁶.3²⁰.5⁹.7⁶.11².13³17.19.23.29.31.41.47.59.71=808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements and plays a starring role in the [Monstrous Moonshine Conjectures]? of Conway and Morton which were subsequently proved by Borcherds.

The largest of the sporadic groups is the Monster group. It has 2⁴⁶.3²⁰.5⁹.7⁶.11².13³17.19.23.29.31.41.47.59.71 = 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements and plays a starring role in the [Monstrous Moonshine Conjectures]? of Conway and Morton which were subsequently proved by Borcherds.

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* [On Finite Simple Groups and their Classification]

*[On Finite Simple Groups and their Classification] (PDF file)

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