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Čunihin's theorem
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(Theorem)
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Remarks
- For $\pi=\{p\}$ , this essentially reduces to the Sylow theorems (with unnecessary hypotheses).
- If $G$ is solvable, it is $\pi$ -separable for all $\pi$ , so such subgroups exist for all $\pi$ . This result is often called Hall's theorem. There is another Hall's theorem, which is similar to this one, can be be found here.
- 1
- Derek J.S. Robinson. A Course in the Theory of Groups, second edition. Springer (1995)
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"Čunihin's theorem" is owned by mathcam. [ full author list (4) | owner history (3) ]
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Cross-references: similar, subgroups, solvable, Sylow theorems, conjugate, contained, primes, finite
This is version 8 of Čunihin's theorem, born on 2002-12-20, modified 2007-10-25.
Object id is 3798, canonical name is VeeCuhininsTheorem.
Accessed 6196 times total.
Classification:
| AMS MSC: | 20D10 (Group theory and generalizations :: Abstract finite groups :: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks) |
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Pending Errata and Addenda
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