14.61 (1999)

Determine all pairs $(\mathscr{S}, G)$, where $\mathscr{S}$ is a semipartial geometry and $G$ is an almost simple flag-transitive group of automorphisms of $\mathscr{S}$. A system of points and lines $(P, B)$ is a semipartial geometry with parameters $(\alpha, s, t, \mu)$ if every point belongs to exactly $t + 1$ lines (two different points belong to at most one line); every line contains exactly $s + 1$ points; for any anti-flag $(a, l) \in (P, B)$ the number of lines containing $a$ and intersecting $l$ is either $0$ or $\alpha$; and for any non-collinear points $a, b$ there are exactly $\mu$ points collinear with $a$ and with $b$.