Characteristic-p validity of the hypercenter characterization

Establish whether the equality $Z^*(L)=nil(L)$ holds for finite-dimensional Lie algebras over fields of prime characteristic.

Background

Theorem 3.4(ii), as cited by the paper, proves in characteristic zero that the hypercenter Z^*(L) equals the nilpotentizer nil(L). The paper does not determine whether this characterization remains valid over fields of prime characteristic, making the positive-characteristic extension an explicit unresolved question.