Wielandt-Kegel theorem


If a finite groupMathworldPlanetmath is the productPlanetmathPlanetmath of two nilpotent subgroupsMathworldPlanetmathPlanetmath, 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 generalizationPlanetmathPlanetmath 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
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