**MSC:**- 20C20 Modular representations and characters
- 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

Koch [5] gives the following lower bound for the number r of relations

given by sums of Lie-monoms of defgree m which are necessary to obtain

a nilpotent LIE-algebra as a factor of a free LIE-algebra with d

generators [8]:

\[ \frac{(m-1)^{m-1}}{m^m}d^m

nilpotent LIE-algebras with a small number of relations. Wisliceny [9]

described a class of systems of relations, called increasing systems

(Erhöhungssysteme), which yield nilpotent LIE-algebras. This was

first done for the case m=2 [9] and later this was generalized by him [10]

and Sauerbier [7], [8] to any m\ge 2.