共查询到20条相似文献,搜索用时 31 毫秒
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Translation planes of order 27 are classified. Various invariants play an important role in a computer search. 相似文献
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In this paper, we describe an exhaustive computer search for all the translation planes of order 49. The search uses the well-known correspondence between translation planes of order 49 and spreads of lines inPG(3,7). We conclude that there are exactly 1347 translation planes of order 49, and give some of their properties including group sizes and 7-ranks. 相似文献
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Lorimer and Rahilly have given constructions for translation planes of order 16. We show that both of these planes have a subplane of order 2 and a group of collineations fixing pointwise which is transitive on the points of –. We show that all such planes of order 16 are isomorphic and that these planes have a number of other properties which are exceptional. 相似文献
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Sharad S Sane 《Journal of Combinatorial Theory, Series A》1985,38(1):91-93
It is well known that the only way of extending a projective plane of order n (conceivable orders are 2, 4 and 10) is adjoining a set of hyperovals to the given projective plane. A converse is proved in this note. It is shown as a corollary that the existence of an extendable plane of order 10 is equivalent to the existence of a quasi-symmetric 2-(111, 12, 10)-design. 相似文献
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R Shull 《Journal of Combinatorial Theory, Series A》1984,37(2):99-120
Let P be a projective plane of order 9 other than one of the four known ones. Then the order of the full collineation group of P is 3a · 5b, where a is a nonnegative integer and b = 0 or 1. 相似文献
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We determine orbit representatives of all proper subplanes generated by quadrangles of a Veblen-Wedderburn (VW) plane Π of order 112 and the Hughes plane Σ of order 112 under their full collineation groups. In Π, there are 13 orbits of Baer subplanes all of which are desarguesian and approximately 3000 orbits of Fano subplanes. In Σ, there are 8 orbits of Baer subplanes all of which are desarguesian, 2 orbits of subplanes of order 3 and at most 408,075 distinct Fano subplanes. This work was motivated by the well-known question: “Does there exist a non-desarguesian projective plane of prime order?” The question remains unsettled. 相似文献
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In this study we show the existence of subplanes of order 3 in Figueroa planes of odd order. 相似文献
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Angelo Sonnino 《Journal of Geometry》1999,66(1-2):187-191
An infinite family of largek-arcs in the inversive plane
over a finite field GF(q), withq 1 (mod 3),q71 orq {17,23, 27,29,41,47,49,53,59} is constructed.Research supported by G.N.S.A.G.A. of C.N.R., project Applicazioni della matematica per la tecnologia e la società, subproject Calcolo simbolico. 相似文献
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Only a few classes of square order planes are known. These are generalized André planes (including Hall planes), flag transitive planes, Hering's planes and Walker's planes. A new class of planes of order 52r, where r is an odd natural number, is constructed and the translation complements of the corresponding planes have been determined. The translation complements divide the sets of distinguished points into 4 orbits of lengths 1, 1, 5r ? 1, and 52r ? 5r and it is of order 5r(5r ? 1)2 if r ≠ 1. In the particular case of r = 1, the translation complement divides the set of distinguished points into two orbits of lengths 6 and 20 and it is of order 480. 相似文献
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N. L. Johnson 《Journal of Geometry》1983,20(1):101-110
In this article we prove the following: Let E denote the group generated by the set of all elations in a non-Desarguesian translation plane π of order 16. Then E is elementary abelian or dihedral of order 6 or 10. If ¦E¦=10 then the set of elation axes defines a derivable net contained in an E-invariant Desarguesian net of degree 7 and in this case π is the Hall plane. Thus, the only translation planes of order 16 to admit at least four elations with distinct axes are the Desarguesian and Hall planes. 相似文献
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Michael J. Kallaher 《Geometriae Dedicata》1973,1(4):415-425
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