The Construction of Translation Planes
نویسندگان
چکیده
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 pla.uer. A plane 1t is given by the construction precisely when 1t is a translation p1ar1e with a coordinatizing :right Veblen-Wedderburn system which is finite-dimensional over its left-operator skewfield. The condition is satisfied by all known translation planes, including all finite translation p1aneso
منابع مشابه
Orthomorphisms and the construction of projective planes
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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