On Lie Algebras with Many Nilpotent Subalgebras

ABSTRACT

Let L be a torsion-free Lie algebra over a commutative domain. L is defined to be S-minimal non-nilpotent if L is not nilpotent but every proper subalgebra of L is nilpotent or its isolator is L. We give a description of the structure of L in the case that L is solvable.

Keywords:

• Isolated subalgebra
• Nilpotent Lie algebra

Mathematics Subject Classification:

• 17B30

ACKNOWLEDGMENT

The authors thank the referee for valuable suggestions.

The author Alexander A. Lashkhi was supported by the NATO C.N.R. Grant 220341 and C.N.R. Short Mobility Grant 140.4 (Rome, Italy 1999–2000).

Dedicated to Professor O. H. Kegel on his 70th birthday.

Notes

Communicated by V. Artamonov.