Innovations in Incidence Geometry

$j,k$-planes of order $4^3$

Norman L. Johnson, Oscar Vega, and Fred W. Wilke

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A new class of translation planes of order 4 3 is constructed and studied. These planes are a generalization of the j -planes discovered by Johnson, Pomareda and Wilke. These j , k -planes may be André replaced and the j , k -planes and the planes obtained by André replacement may be derived. There are thirteen new planes constructed and classified. Using ‘regular hyperbolic covers’, there are some new constructions of flat flocks of Segre varieties by Veronesians.

Article information

Innov. Incidence Geom., Volume 2, Number 1 (2005), 1-34.

Received: 31 March 2005
Accepted: 8 November 2005
First available in Project Euclid: 28 February 2019

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Zentralblatt MATH identifier

Primary: 05B25: Finite geometries [See also 51D20, 51Exx] 20H30: Other matrix groups over finite fields 51E15: Affine and projective planes

translation planes homology groups flat flocks


Johnson, Norman L.; Vega, Oscar; Wilke, Fred W. $j,k$-planes of order $4^3$. Innov. Incidence Geom. 2 (2005), no. 1, 1--34. doi:10.2140/iig.2005.2.1.

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