Steiner systems $S(v,k,k-1)$: components and rank

For an arbitrary Steiner system $S(v,k,t)$, we introduce the concept of a component as a subset of a system which can be transformed (changed by another subset) without losing the property for the resulting system to be a Steiner system $S(v,k,t)$. Thus, a component allows one to build new Steiner systems with the same parameters as an initial system. For an arbitrary Steiner system $S(v,k,k-1)$, we provide two recursive construction methods for infinite families of components (for both a fixed and growing k). Examples of such components are considered for Steiner triple systems $S(v,3,2)$ and Steiner quadruple systems $S(v,4,3)$. For such systems and for a special type of so-called normal components, we find a necessary and sufficient condition for the 2-rank of a system (i.e., its rank over $\mathbb F_2$) to grow under switching of a component. It is proved that for $k\ge5$ arbitrary Steiner systems $S(v,k,k-1)$ and $S(v,k,k-2)$ have maximum possible 2-ranks.