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Čunihin's theorem (Theorem)
Theorem 1 (Čunihin)   Let $ G$ be a finite, $ \pi$-separable group, for some set $ \pi$ of primes. Then

Remarks

  1. For $ \pi=\{p\}$, this essentially reduces to the Sylow theorems (with unnecessary hypotheses).
  2. 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.

Bibliography

1
Derek J.S. Robinson. A Course in the Theory of Groups, second edition. Springer (1995)



"Čunihin's theorem" is owned by mathcam. [ full author list (4) | owner history (3) ]
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See Also: Hall subgroup

Also defines:  Hall's theorem
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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 5388 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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