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examples of finite simple groups
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(Example)
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This entry is under construction. If I take too long to finish it, nag me about it, or fill in the rest yourself.
All groups considered here are finite.
It is now widely believed that the classification of all finite simple groups up to isomorphism is finished. The proof runs for at least 10,000 printed pages, and as of the writing of this entry, has not yet been published in its entirety.
There are twenty-six sporadic groups (no more, no less!) that do not fit into any of the infinite sequences of simple groups considered above. These often arise as the group of automorphisms of strongly regular graphs.
- Mathieu groups.
- Janko groups.
- The baby monster.
- The monster.
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"examples of finite simple groups" is owned by mathcam. [ full author list (4) | owner history (1) ]
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(view preamble)
Cross-references: Janko groups, regular graphs, automorphisms, sequences, infinite, projective special linear groups, commutators, centers, sources, polynomial, simplicity of the alternating groups, argument, simple, index, transposition, bijection, odd, even, permutation, odd permutations, homomorphism, kernel, normal subgroup, symmetric group, even permutations, abelian, Cauchy's theorem, order, cyclic groups, isomorphism, simple groups, finite, groups
There are 13 references to this entry.
This is version 12 of examples of finite simple groups, born on 2002-11-04, modified 2004-11-17.
Object id is 3568, canonical name is ExamplesOfFiniteSimpleGroups.
Accessed 10657 times total.
Classification:
| AMS MSC: | 20A05 (Group theory and generalizations :: Foundations :: Axiomatics and elementary properties) | | | 20E32 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Simple groups) |
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Pending Errata and Addenda
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