Vol. 4, No. 1, 2006

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Stable planes with a point transitive abelian group

Andreas Wörner

Vol. 4 (2006), No. 1, 53–61
Abstract

We consider stable planes E = (P,) admitting an abelian group Δ which acts (sharply) transitively on the point set P. Known examples are the so-called arc planes with Δ = 2 (H. Groh, 1979), affine translation planes and shift planes. We examine the possible actions of Δ on the line space and use the results in order to characterize affine shift planes and translation planes.

Keywords
stable planes, abelian group action, arc planes
Mathematical Subject Classification 2000
Primary: 51H10
Milestones
Received: 21 April 2006
Accepted: 3 July 2006
Authors
Andreas Wörner
Mathematisches Institut, Fachbereich Mathematik und Informatik
Westfälische Wilhelms-Universität Münster
Einsteinstraße 62
48149 Münster
Germany