The purpose of this interlude is to provide a set of generators for the special orthogonal
groups SO (V, q)= SOq, starting from the Liealgebra so (V, q). Typically one creates …

For a finite group GG, let σ (G) σ(G) be the number of subgroups of GG and σ ι (G) σ_ι(G) the
number of isomorphism types of subgroups of G G. Let L= L r (pe) L=L_r(p^e) denote a …

Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of
type F 4, we construct a rank three geometry. The main property of this new geometry is that …

Rank one groups are a class of doubly transitive groups that are natural generalizations of
the groups SL2 (k). The most interesting examples arise from exceptional algebraic groups …

As one can see, the title of this thesis is:'A study of buildings of low rank'. The theory of
buildings is developed in the early'60s by Jacques Tits. The aim was to study various …