Existence of abelian ideals of small prime power order in nilpotent Lie ring
- Existence of abelian normal subgroups of small prime power order (see more facts related to that)
- Lower bound on order of maximal among abelian ideals in terms of order of nilpotent Lie ring
- Finite nilpotent Lie ring implies every ideal contains ideals of all orders dividing its order
Outline: We use Fact (1) to show that there is an abelian ideal of order at least , and then use Fact (2) to find within that an abelian ideal of order exactly .