Lenz-Barlotti classes of semi-classical ordered projective planes
نویسنده
چکیده
This paper concerns a generalization of Moulton planes. We consider these semi-classical projective planes over half-ordered fields and completely determine their Lenz-Barlotti classes in the case of finite planes and of ordered planes. We also obtain a characterization of the Desarguesian planes among the semi-classical planes in terms of linear transitivity. These results are applied to (topological) 2-dimensional semi-classical projective planes.
منابع مشابه
On finite projective planes in Lenz–Barlotti class at least I.3
We establish the connections between finite projective planes admitting a collineation group of Lenz–Barlotti type I.3 or I.4, partially transitive planes of type (3) in the sense of Hughes, and planes admitting a quasiregular collineation group of type (g) in the Dembowski– Piper classification; our main tool is an equivalent description by a certain type of di¤erence set relative to disjoint ...
متن کاملOn finite projective planes in Lenz-Barlotti class at least 1.3
We establish the connections between finite projective planes admitting a collineation group of Lenz-Barlotti type 1.3 or 1.4, partially transitive planes of type (3) in the sense of Hughes, and planes admitting a quasiregular collineation group of type (g) in the DembowskiPiper classification; our main tool is an equivalent description by a certain type of difference set relative to disjoint s...
متن کاملPlanar Functions and Planes of Lenz-Barlotti Class II
Planar functions were introduced by Dembowski and Ostrom ([4]) to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a question posed in [4]. These planar f...
متن کاملOn the Lenz-Barlotti Classification of Projective Planes
Theorem 1 implies that there does not exist any finite projective plane of Lenz type III . This completes results of Lff~V.BIYRG [11 and 12], C o F ~ [2], YAQUB [17], and HERr~G [6]. Theorem 2 implies that there does not exist any finite projective plane of Lenz-Barlotti type 1.6 or II.3. This result is due to YAQU~ [15 and 16], J6~sso~ [9], Lt~WBV~O [10], and CoFM~ [3]. Both theorems will be p...
متن کاملOn collineation groups of finite planes
From the Introduction to P. Dembowski’s Finite Geometries, Springer, Berlin 1968: “ . . . An alternative approach to the study of projective planes began with a paper by BAER 1942 in which the close relationship between Desargues’ theorem and the existence of central collineations was pointed out. Baer’s notion of (p, L)–transitivity, corresponding to this relationship, proved to be extremely f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 16 شماره
صفحات -
تاریخ انتشار 1997