Linear spaces with flag-transitive automorphism groups
Authors give a classification of the pairs (S,G) where S is a non-trivial finite linear space and G is a group of automorphisms acting transitively on the flags of S. The authors refer to linear space S as to a finite incidence structure of points and lines such that any two points are incident with exactly one line and some non-triviality conditions are satisfied. A flag of S is an incident point-line pair. The authors give a full classification of the pairs (S,G) in the case when the dimension is greater than 1. In this case they consider two possibilities: a) G is almost simple; that is, G has a non-Abelian simple normal subgroup N such that \(N\trianglelefteq G\leq Aut N\). b) G is affine. If \(G\leq A\Gamma L(1,q)\) (where \(A\Gamma\) L(1,q) is the group of 1- dimensional semilinear affine transformations, S has \(q=p^ a\) points (p prime)) the authors are unable to present full classification.
scientific article; zbMATH DE number 4161559