Theorem of Tits

The Tits theorem states that for certain symmetrical objects called buildings, all possible symmetries (or automorphisms) can be broken down into simpler, well-understood transformations. Specifically, it shows that the group of all these symmetries is generated by those that preserve key structural parts called residues and chambers. In essence, it helps mathematicians understand and classify the symmetries of these complex structures by revealing that they are built from basic, fundamental symmetry moves. This theorem is fundamental in the study of geometric structures related to algebraic groups and group theory.