Direct sum decomposition of geometries based on maximal subgroups (Q1879086)

In the theory of incidence geometries due to Tits and Buekenhout, geometries are based on groups and collections of subgroups. The author is concerned with the case where all the subgroups used are maximal (so that the group acts primitively on elements of each type). He studies the decomposition of geometries into direct sums; in particular, he determines the full direct sum decomposition if the underlying group is a finite solvable group.