On the classification of flag-transitive \(c. c^*\)-geometries (Q1290867)

The authors list all known examples of (finite) flag-transitive geometries with linear diagram \(c.c^*\) with the property that the point stabilizer (which is a doubly transitive group, hence of affine type or almost simple) is an almost simple group. They conjecture that this list is complete. In order to show such a thing, the authors suggest to study a minimal counter example. In the paper under review they show that such an example has a group of Lie type as flag-transitive group. They also indicate that this might make the conjecture feasible. The proof of this important result is very group related, and consists mainly of a case-by-case analysis to rule out each sporadic simple group.