ELA, Volume 16, pp. 429-434, December 2007, abstract.

Class, Dimension and Length in Nilpotent Lie Algebras 

Lisa Wood Bradley and Ernie L. Stitzinger 

The problem of finding the smallest order of a p-group of a 
given derived length has a long history. Nilpotent Lie algebra 
versions of this and related problems are considered. Thus, the 
smallest order of a p-group is replaced by the smallest dimension 
of a nilpotent Lie algebra. For each length t, an upper bound for 
this smallest dimension is found. Also, it is shown that for each 
t>=5 there is a two generated Lie algebra of nilpotent class 
d =  21(2^{t-5}) whose derived length is t. For two generated Lie 
algebras, this result is best possible. Results for small t are 
also found. The results are obtained by constructing Lie algebras 
of strictly upper triangular matrices.