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Translation Planes of Dimension Two with Odd Characteristic

Published online by Cambridge University Press:  20 November 2018

T. G. Ostrom
T. G. Ostrom*
Affiliation:
Washington State University, Pullman, Washington
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A translation plane of dimension d over its kernel K = GF(q) can be represented by a vector space of dimension 2d over K. The lines through the zero vector form a “spread”; i.e., a class of mutually independent vector spaces of dimension d which cover the vector space.

The case where d = 2 has aroused the most interest. The more exotic translation planes tend to be of dimension two; a spread in this case can be interpreted as a class of mutually skew lines in projective three-space.

The stabilizer of the zero vector in the group of collineations is a group of semi-linear transformations and is called the translation complement. The subgroup consisting of linear transformations is the linear translation complement.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 5 , 01 October 1980 , pp. 1114 - 1125
Copyright
Copyright © Canadian Mathematical Society 1980

References

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