Some translation planes with elations which are not translations

Finite generalized Hall planes possessing elations which are not translations for more than one centre on the translation line are investigated. The existence of such elations is related to the structure of certain coordinate systems and the precise set of points that are centres of such elations is...

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Bibliographic Details
Main Author: Rahilly, Alan
Format: Book Chapter
Language:English
Subjects:
Baer Subplane
Collineation Group
Combinatorial Mathematic
Frobenius Group
Translation Plane
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Summary:Finite generalized Hall planes possessing elations which are not translations for more than one centre on the translation line are investigated. The existence of such elations is related to the structure of certain coordinate systems and the precise set of points that are centres of such elations is determined. A method of constructing planes possessing such elations is elaborated and then applied to construct planes of order 24n for each n≥1.
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0069558