Abstract: Earlier, we saw that finite groups can be taken apart through the composition series, in terms of simple finite groups, that is groups without normal subgroups. Remarkably the infinitude of simple groups is amenable to a complete classification. Indeed, most simple groups can be understood as finite elements of Lie groups, with parameters belonging to finite Galois fields. Their construction relies on the Chevalley basis of the Lie algebra, as well as on the topology of its Dynkin diagram. The remaining simple groups do not follow this pattern; they are the magnificent 26 sporadic groups. A singular achievement of modern mathematics was to show this classification to be complete.
Publication Year: 2010
Publication Date: 2010-05-13
Language: en
Type: book-chapter
Indexed In: ['crossref']
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