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… 
1 Citations

Derived length and nildecomposable Lie algebras

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

References

SHOWING 1-10 OF 11 REFERENCES

Groups St Andrews 1997 in Bath, I: Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators

The group U_n(F) of all nxn unipotent upper-triangular matrices over F has derived length d := Ceiling(log_2 (n)), equivalently 2^{d-1} < n <= 2^d. We prove that U_n(F) has a 3-generated subgroup of

A Contribution to the Theory of Groups of Prime‐Power Order

On Some Properties of Groups Whose Orders are Powers of Primes

dim d s = 2 if s is congruent to 0 mod 3, s = n − 1

    Subgroups of the upper triangular matrix group with maximal derived length and minimal number of generators. Groups St. Andrews in Bath

    • Lecture Notes Ser
    • 1997

    Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society

    • Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society
    • 2007

    On the solvable length of groups of primepower order

    • Bull. Aus. Math. Soc
    • 1999

    Since 3 does not divide s, this commutator equals either F i,s+i or −F j,q+j , depending on 1 ≤ i < j ≤ 3

      Subgroups of the upper triangular matrix group with maximal derived length and minimal number of generators

      • Groups St. Andrews in Bath,
      • 1997

      If following hold 1. dim d s = 3 if s is not congruent to 0 mod 3, s = n − 2