Generation of groups by rank-2 tori

Let k be a field of characteristic different from 2 and 3. In this paper, we study the number of rank-2 k-tori required (in fact exhibit such tori explicitly) for the generation of groups of type A₂, G₂ and F₄ arising from division algebras and subgroups of type D₄ of Aut(A), for A an Albert division algebra, over infinite perfect fields.