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  "body": "\n## Statement\n\nEach finite [[simple group|0YMYMNQ0QZ]] is isomorphic to one of the following groups:\n\n1. a [[cyclic group|0KVGH0J5B3]] $\\mathbb{Z}/p\\mathbb{Z}$ of prime order $p$;\n2. an [[alternating group|0Z5905Q73D]] $A_n$ with $n \\geq 5$;\n3. a group of Lie type;\n4. one of $26$ sporadic groups.\n\n## Remarks\n\nThe groups of Lie type form infinite families, for example the groups $\\mathrm{PSL}_n(\\mathbb{F}_q)$, with a few exceptions for small $n$ and $q$.\nSome authors count the Tits group as a $27$th sporadic group, because it is not strictly of Lie type.\nThe largest sporadic group is the Monster group.\nThe proof consists of tens of thousands of pages in several hundred journal articles.\n\n## History\n\nDaniel Gorenstein announced in 1983 that the classification was complete, but this was premature.\nThe gap was the case of the quasithin groups.\nMichael Aschbacher announced the completed proof in 2004, after Aschbacher and Stephen Smith published a proof of $1221$ pages for this case.\n\n## Explanations\n\n### L1 human\n\nThe theorem lists all the finite simple groups.\nMost of them come in a few infinite families, and only $26$ are special cases.\nSince each finite group is built from simple groups, this list is a map of all the building blocks.\n",
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