Abstract
It is proved that if a (ℤ/p ℤ)-graded Lie algebra L, where p is a prime, has exactly d nontrivial grading components and dim L 0 = m, then L has a nilpotent ideal of d-bounded nilpotency class and of finite (m,d)-bounded codimension. As a consequence, Jacobson's theorem on constant-free nilpotent Lie algebras of derivations is generalized to the almost constant-free case. Another application is for Lie algebras with almost fixed-point-free automorphisms.
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