## Abstract

The following theorem will be proved: THEOREM. Let (P,) be a linear space with dimension dim(P,) ≥ 2, such that each line contains at least three points. Let further Γ ≤ Aut(P,) be a two - transitive group of collineations on the point set P, such that every automorphism γ ε Γ fixing one flag (p,L), fixes all lines through p. Then (P,) is a desarguesian affine space and Γ contains the whole group of dilatations of (P,). Moreover one can define an addition and a multiplication on the point set, such that (P,+,-) is a nearfield, the line {Mathematical expression} joining the neutral elements is a normal subfield and Γ consists of the affine transformations x → a + mx, m≠ 0 and= Γ(K).

Original language | German |
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Pages (from-to) | 55-68 |

Number of pages | 14 |

Journal | Journal of Geometry |

Volume | 32 |

Issue number | 1-2 |

DOIs | |

State | Published - Aug 1988 |