The construction of translation planes from projective spaces
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چکیده
منابع مشابه
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The Construction of Translation Planes
Can eve.ry (non-Desarguest.. an) projee.,tJVe p~' ~ imbedded (in some natural, g~anet.ric ff.hion) in af1J8sarguesian) projective space? The Ite,titn is ne...WI~.ut .. ,trnp .. · ortant, for, if the answer is yes, tfo entirely SEijifia'Wt fields of research can be united~ 1his paper ;p~1des. conceptually simple geometric construction 1vh1dti',Y1elds an affirmative answer for a broad class of pl...
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We discuss a simple computational method for the construction of finite projective planes. The planes so constructed all possess a special group of automorphisms which we call the group of translations, but they are not always translation planes. Of the four planes of order 9, three admit the additive group of the field GF (9) as a group of translations, and the present construction yields all ...
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From a projective plane Π with involutory homology τ one constructs an incidence system Π/τ having as points and blocks the 〈τ〉-orbits of length 2 on the points and lines of Π, and with incidence inherited from Π. Such incidence systems satisfy certain properties which, when taken as axioms, define the class of homology semibiplanes. We describe how one determines, in principle, whether a given...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1964
ISSN: 0021-8693
DOI: 10.1016/0021-8693(64)90010-9