Wielandt-Kegel theorem
Theorem.
If a finite group is the product of two nilpotent subgroups, then it is solvable.
That is, if H and K are nilpotent subgroups of a finite group G, and G=HK, then G is solvable.
This result can be considered as a generalization of Burnside’s p-q Theorem (http://planetmath.org/BurnsidePQTheorem), because if a group G is of order pmqn, where p and q are distinct primes, then G is the product of a Sylow p-subgroup (http://planetmath.org/SylowPSubgroup) and Sylow q-subgroup, both of which are nilpotent.
Title | Wielandt-Kegel theorem |
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Canonical name | WielandtKegelTheorem |
Date of creation | 2013-03-22 16:17:37 |
Last modified on | 2013-03-22 16:17:37 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 11 |
Author | yark (2760) |
Entry type | Theorem |
Classification | msc 20D10 |
Synonym | Kegel-Wielandt theorem |