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Transitive affine planes admitting elations |
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| Authors: | J B Fink N L Johnson F W Wilke |
| Institution: | 1. Mathematics Dept., Kalamazoo College, Kalamazoo, Mich. 2. Mathematics Dept., University of Iowa, Iowa City, Ia. 3. Mathematics Dept., University of Missouri, St. Louis, Mo. |
| Abstract: | Affine planes which admit a point transitive collineation group and at least one affine elation are considered. Such a plane is shown to be (A,?∞)-transitive for some point A on ?t8 and to be a translation plane if at least two distinct elation centers exist. If the plane has at least (order)1/2+1 distinct elation centers and the group generated by the elations is nonsolvable then the plane is either Desarguesian or Lüneburg-Tits. |
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