Pencils of translation ovals in translation planes

D. G. Glynn; G. F. Steinke

doi:10.1007/bf01265323

Pencils of translation ovals in translation planes

Geometriae Dedicata ◽

10.1007/bf01265323 ◽

1994 ◽

Vol 51 (2) ◽

pp. 113-121 ◽

Cited By ~ 1

Author(s):

D. G. Glynn ◽

G. F. Steinke

Keyword(s):

Translation Planes ◽

Translation Ovals

Compact spreads and compact translation planes over locally compact fields

Journal of Geometry ◽

10.1007/bf01231026 ◽

1989 ◽

Vol 36 (1-2) ◽

pp. 110-116 ◽

Cited By ~ 8

Author(s):

Rainer L�wen

Keyword(s):

Translation Planes ◽

Locally Compact

On the compatibility of planar and nonplanar involutions in translation planes

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ◽

10.1007/bf02941863 ◽

1982 ◽

Vol 52 (1) ◽

pp. 16-28 ◽

Cited By ~ 1

Author(s):

Norman L. Johnson

Keyword(s):

Translation Planes

Translation planes admitting many homologies

Journal of Geometry ◽

10.1007/bf01228056 ◽

1994 ◽

Vol 49 (1-2) ◽

pp. 117-149 ◽

Cited By ~ 1

Author(s):

Norman L. Johnson ◽

Rolando Pomareda

Keyword(s):

Translation Planes

Quartic Groups in Translation Planes

Handbook of Finite Translation Planes - Pure and Applied Mathematics ◽

10.1201/9781420011142.ch68 ◽

2007 ◽

pp. 509-514

Keyword(s):

Translation Planes

Unitals in Translation Planes

Handbook of Finite Translation Planes ◽

10.1201/9781420011142-90 ◽

2007 ◽

pp. 671-682

Keyword(s):

Translation Planes

Translation Planes with Large Homology Groups

Handbook of Finite Translation Planes ◽

10.1201/9781420011142-24 ◽

2007 ◽

pp. 181-186

Keyword(s):

Translation Planes ◽

Homology Groups

On Transposed Translation Planes

Open Journal of Discrete Mathematics ◽

10.4236/ojdm.2012.21007 ◽

2012 ◽

Vol 02 (01) ◽

pp. 35-43

Author(s):

K. Satyanarayana ◽

K. V. V. N. S. Sundari Kameswari

Keyword(s):

Translation Planes

On the Ubiquity of Denniston-Type Translation Ovals in Generalized André Planes

Combinatorics '90 - Recent Trends and Applications, Proceedings of the Conference on Corn binatorics, Gaeta - Annals of Discrete Mathematics ◽

10.1016/s0167-5060(08)70920-8 ◽

1992 ◽

pp. 279-296 ◽

Cited By ~ 2

Author(s):

V. Jha ◽

N.L. Johnson

Keyword(s):

Translation Ovals

On Permutation Polynomials and Derivable Translation Planes

Finite Fields and Applications ◽

10.1007/978-3-642-56755-1_33 ◽

2001 ◽

pp. 428-436

Author(s):

Rita Vincenti

Keyword(s):

Permutation Polynomials ◽

Translation Planes

Collineation Groups of Generalized André Planes

Canadian Journal of Mathematics ◽

10.4153/cjm-1969-036-7 ◽

1969 ◽

Vol 21 ◽

pp. 358-369 ◽

Cited By ~ 10

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).