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Abstract
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This article is a study of arbitrary derivable nets. These nets are known to be embeddable into
-dimensional
projective spaces over skewfields, and may be represented as pseudo-regulus nets in a
classical manner. However, their typology is not well known. This article gives a
classification of derivable nets by comparing such nets to any given classical
pseudo-regulus net. There are four classes and examples of each are given. A number of
applications of this material are discussed.
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Keywords
flocks of cones, twisted hyperbolic flocks, derivable nets,
translation planes, generalized quadrangles, quaternion
division rings, cyclic division rings, André and Ostrom
extensions
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Mathematical Subject Classification
Primary: 51A05, 51A40
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Milestones
Received: 9 November 2021
Accepted: 17 January 2022
Published: 28 May 2022
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