Alphabeta MathHow statement and proof provenance work
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The O'Nan-Scott theorem reduces finite primitive-group questions to socle types
The practical value of the O'Nan-Scott theorem is reduction. Once a finite primitive permutation group is assigned a socle type, many structural and algorithmic questions can be handled case by case inside the affine, almost-simple, diagonal, product-action, or twisted-wreath branches instead of starting from an arbitrary primitive action.
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Sources
- Leonard H. Soicher, Primitive permutation groups (standard reference, not scraped)