scholarly journals Orthogonal Spreads and Translation Planes

2018 ◽  
Author(s):  
William M. Kantor
Keyword(s):  
Translation Planes

Compact spreads and compact translation planes over locally compact fields

1989 ◽  
Vol 36 (1-2) ◽  
pp. 110-116 ◽  
Author(s):  
Rainer L�wen
Keyword(s):  
Translation Planes ◽  
Locally Compact

On the compatibility of planar and nonplanar involutions in translation planes

1982 ◽  
Vol 52 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Norman L. Johnson
Keyword(s):  
Translation Planes

Translation planes admitting many homologies

1994 ◽  
Vol 49 (1-2) ◽  
pp. 117-149 ◽  
Author(s):  
Norman L. Johnson ◽  
Rolando Pomareda
Keyword(s):  
Translation Planes

Unitals in Translation Planes

2007 ◽  
pp. 671-682
Keyword(s):  
Translation Planes

scholarly journals On Transposed Translation Planes

2012 ◽  
Vol 02 (01) ◽  
pp. 35-43
Author(s):  
K. Satyanarayana ◽  
K. V. V. N. S. Sundari Kameswari
Keyword(s):  
Translation Planes

On Permutation Polynomials and Derivable Translation Planes

2001 ◽  
pp. 428-436
Author(s):  
Rita Vincenti
Keyword(s):  
Permutation Polynomials ◽  
Translation Planes

Collineation Groups of Generalized André Planes

1969 ◽  
Vol 21 ◽  
pp. 358-369 ◽  
Author(s):  
David A. Foulser
Keyword(s):  
Main Question ◽  
Translation Planes ◽  
Hall Plane ◽  
Collineation Groups

In a previous paper (5), I constructed a class of translation planes, called generalized André planes or λ-planes, and discussed the associated autotopism collineation groups. The main question unanswered in (5) is whether or not there exists a collineation η of a λ-plane Π which moves the two axes of Π but does not interchange them.The answer to this question is “no”, except if Π is a Hall plane (or possibly if the order n of Π is 34) (Corollary 2.8). This result makes it possible to determine the isomorphisms between λ-planes. More specifically, let Π and Π′ be two λ-planes of order n coordinatized by λ-systems Qand Q′, respectively. Then, except possibly if n = 34, Π and Π′ are isomorphic if and only if Q and Q′ are isotopic or anti-isotopic (Corollary 2.13). In particular, Π is an André plane if and only if Q is an André system (Corollary 2.14).

Conjecture of D. R. Hughes Extended to Generalized André Planes

1970 ◽  
Vol 22 (3) ◽  
pp. 701-704
Author(s):  
M. L. Narayana Ra
Keyword(s):  
Original Problem ◽  
Translation Planes ◽  
Alternate Proof ◽  
Collineation Groups

In 1967 Foulser [1] defined a class of translation planes, called generalized André planes or λ-planes and discussed the associated autotopism collineation groups. While discussing these collineation groups he raised the following question:“Are there collineations of a λ plane which move the axes but do not interchange them?”.In this context, Foulser mentioned a conjecture of D. R. Hughes that among the André planes, only the Hall planes have collineations moving the axes without interchanging them. Wilke [4] answered Foulser's question partially by showing that the conjecture of Hughes is indeed correct. Recently, Foulser [2] has shown that possibly with a certain exception the Hall planes are the only generalized André planes which have collineations moving the axes without interchanging them. Our aim in this paper is to give an alternate proof, which is completely general, and is in the style of the original problem.

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