A characterization of certain elation Laguerre planes
نویسنده
چکیده
We characterize the non-classical 4-dimensional elation Laguerre planes as precisely those 4-dimensional Laguerre planes of Kleinewillinghöfer type I.D.1. Furthermore, in the class of 2or 4-dimensional Laguerre planes or finite Laguerre planes of odd order, the non-miquelian elation Laguerre planes are precisely the Laguerre planes of Kleinewillinghöfer type D. MSC 2000: 51H15, 51B15, 51E25
منابع مشابه
Sisters of some 4-dimensional elation Laguerre planes
We give an explicit description of some sisters of 4-dimensional elation Laguerre planes of group dimension 10 with respect to points of the Laguerre planes. In this way we obtain the first concrete examples of 4-dimensional Laguerre planes of group dimensions 8 and 7 and of 4-dimensional Laguerre planes that are not elation Laguerre planes. MSC 2000: 51H15.
متن کاملElation Laguerre planes of order p2 that admit an automorphism group of order p2 in the elation complement
Following the program for finite translation planes to construct such planes from collineation groups in the translation complement a search for nonMiquelian Laguerre planes of odd order is initiated. In this note finite Laguerre planes of order p2 , P a prime, are investigated. If such a Laguerre plane .c admits a circle-transitive elation group and an automorphism group of order p2 in the ela...
متن کاملFinite elation Laguerre planes admitting a two-transitive group on their set of generators
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 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. As a conse...
متن کاملMore on Kleinewillinghöfer types of flat Laguerre planes
Polster and Steinke [Result. Math., 46 (2004), 103–122] determined the possible Kleinewillinghöfer types of flat Laguerre planes. These types reflect transitivity properties of groups of certain central automorphisms. We exclude three more types from the list given there with respect to Laguerre homotheties. This yields a complete determination of all possible single types with respect to Lague...
متن کاملThe Symmetry Axioms in Laguerre Planes
We introduce two axioms in Laguerre geometry and prove that they provide a characterization of miquelian planes over fields of the characteristic different from 2. They allow to describe an involutory automorphism that sheds some new light on a Laguerre inversion as well as on a symmetry with respect to a pair of generators.
متن کامل