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Jill C. D. S. Yaqub 《Archiv der Mathematik》1961,12(1):146-150
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Summary The theory of linear representations of projective planes developed by Bruck and one of the authors (Bose) in two earlier
papers [J. Algebra1 (1964), pp. 85–102 and4 (1966), pp. 117–172] can be further extended by generalizing the concept of incidence adopted there. A linear representation is obtained for
a class of non-Desarguesian projective planes illustrating this concept of generalized incidence. It is shown that in the
finite case, the planes represented by the new construction are derived planes in the sense defined by Ostrom [Trans. Amer.
Math Soc.111 (1964), pp. 1–18] and Albert [Boletin Soc. Mat. Mex,11 (1966), pp, 1–13] of the dual of translation planes which can be represented in a 4-space by the Bose-Bruck construction. An analogous interpretation
is possible for the infinite case.
This research was sponsored by the National Science Foundation under Grant No. GP-8624, and the U.S. Air Force Office of Scientific
Research under Grant No. AFOSR-68-1406.
This research was conducted while the author was visiting professor at the University of North Carolina at Chapel Hill. His
research was also partially supported by C.N.R.
Entrata in Redazione il 28 maggio 1970. 相似文献
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Franz Kalhoff 《Geometriae Dedicata》1992,43(2):225-231
Dress and Wenzel have codified the notion of the Tutte group of a matroid and have determined the Tutte group of projective spaces over skew fields and of finite projective planes. In this note we shall examine the Tutte group of arbitrary projective planes. 相似文献
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E. Mendelsohn 《Journal of Geometry》1974,4(2):161-165
In [7] the author showed the existence of projective plane pathological with respect to the collineation groups of its sub and quotient planes. Similar pathologies are obtainable with respect to collineation groups of associated affine planes. (i.e. the affine planes obtained by distinguishing a line as the line at infinity) as expressable in the following theorem. 相似文献
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V. V. Vdovin 《Geometriae Dedicata》1991,39(1):115-123
An attempt to define a finite presentation for projective planes by analogy to finitely presented groups has been made in [9]. In this article we suggest another definition for a presentation of projective planes: constructively presented planes. A few simple results about such planes and an example of constructively presented planes with nonsolvable word problem are given.This paper was written while the author was visiting the University of Bergen, Norway. 相似文献
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We find all stable projective planes with finite topology which are properly embedded in , where is a discrete subgroup of translations in . Here stable means second order minimum of the area. The surfaces we obtain are a quotient of the helicoid and quotients of the doubly periodic Scherk surfaces.
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