Connected algebraic subgroups of groups of birational transformations not contained in a maximal one - Fong, Pascal; Zikas, Sokratis (Comptes Rendus. Mathématique)
We prove that for each $n\ge 2$, there exist a ruled variety $X$ of dimension $n$ and a connected algebraic subgroup of $Bir(X)$ which is not contained in a maximal one.