Lie \(p\)-algebras of finite \(p\)-subalgebra rank (Q1599473)

We say that a Lie \(p\)-algebra \(L\) has finite \(p\)-subalgebra rank if the minimal number of generators required to generate every finitely generated \(p\)-subalgebra is uniformly bounded by some integer \(r\). This paper is concerned with the following problem: does \(L\) being of finite \(p\)-subalgebra rank force \(\text{ad}(L)\) to be finite dimensional? Although this seems unlikely in general, the author shows that this is indeed the case for Lie \(p\)-algebras in a large class including all locally, residually, and virtually soluble Lie \(p\)-algebras.