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.