# CLASS, DIMENSION AND LENGTH IN NILPOTENT LIE ALGEBRAS ∗

@article{Bradley2007CLASSDA, title={CLASS, DIMENSION AND LENGTH IN NILPOTENT LIE ALGEBRAS ∗}, author={Lisa Wood Bradley and Ernest Stitzinger}, journal={Electronic Journal of Linear Algebra}, year={2007}, volume={16}, pages={35} }

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 =2 1(2 t−5 ) whose derived length is t. For two…

## One Citation

### Derived length and nildecomposable Lie algebras

- Mathematics
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We study the minimal dimension of solvable and nilpotent Lie algebras over a field of characteristic zero with given derived length $k$. This is motivated by questions on nildecomposable Lie algebras…

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