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11.70 (1990)

Partially Solved

Let $F$ be an infinite field or a skew-field.
$\qquad$ a) Find all transitive subgroups of $PGL(2, F)$ acting on the projective line $F \cup \{\infty\}$.
$\qquad$ b) What conditions on the subring $R$ of $F$ will ensure that $\text{PGL}(d+1, R)$ is flag-transitive on the projective $d$-space $\text{PG}(d, F)$?
$\qquad$ c) What are the flag-transitive subgroups of $PGL(d + 1, F)$?
$\qquad$ d) What subgroups of $PGL(d + 1, F)$ are 2-transitive on the points of $PG(d, F)$?

Contributor: P. M. Neumann, C. E. Praeger

Progress

b) Such necessary and sufficient conditions are given in (S. A. Zyubin, Siberian Electron. Math. Rep., 11 (2014), 64–69 (Russian)).

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