Wielandt-Kegel theorem
Theorem.
If a finite group is the product
of two nilpotent subgroups
,then it is solvable.
That is, if and are nilpotent subgroups of a finite group ,and , then is solvable.
This result can be considered asa generalization of Burnside’s - Theorem (http://planetmath.org/BurnsidePQTheorem),because if a group is of order , where and are distinct primes, then is the product of a Sylow -subgroup (http://planetmath.org/SylowPSubgroup) and Sylow -subgroup, both of which are nilpotent.