Vol. 13, No. 1, 2013

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Finite elation Laguerre planes admitting a two-transitive group on their set of generators

Günter F. Steinke and Markus Stroppel

Vol. 13 (2013), No. 1, 207–223

We investigate finite elation Laguerre planes admitting a group of automorphisms that is two-transitive on the set of generators. We exclude the sporadic cases of socles in two-transitive groups, as well as the alternating and Suzuki groups and the cases with abelian socle (except for the smallest ones, where the Laguerre planes are Miquelian of order at most four). The remaining cases are dealt with in a separate paper. We prove that a finite elation Laguerre plane is Miquelian if its automorphism group is two-transitive on the set of generators. Equivalently, each translation generalized quadrangle of order q with a group of automorphisms acting two-transitively on the set of lines through the base point is classical.

Mathematical Subject Classification 2010
Primary: 20B20, 51B15, 51E12, 51E25
Received: 8 March 2013
Accepted: 28 July 2013
Günter F. Steinke
School of Mathematics and Statistics
University of Canterbury
Private Bag 4800
Christchurch 8140
New Zealand
Markus Stroppel
LExMath, Fakultät für Mathematik und Physik
Universität Stuttgart
70550 Stuttgart