Vol. 2, No. 1, 2005

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

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

Vol. 2 (2005), No. 1, 1–34
DOI: 10.2140/iig.2005.2.1
Abstract

A new class of translation planes of order 43 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.

Keywords
translation planes, homology groups, flat flocks
Mathematical Subject Classification 2000
Primary: 05B25, 20H30, 51E15
Milestones
Received: 31 March 2005
Accepted: 8 November 2005
Authors
Norman L. Johnson
University of Iowa
IA
United States
Oscar Vega
Department of Mathematics
California State University, Fresno
Peters Business Building
5245 North Backer Avenue M/S PB108
Fresno, CA 93740-8001
United States
Fred W. Wilke