A new family of locally compact 4-dimensional translation planes admitting a 7-dimensional collineation group

Author:

Ortleb Sigrun1

Affiliation:

1. Fachbereich Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany. Email:

Abstract

Abstract The present paper contains the construction of a family of 4-dimensional translation planes with a 7-dimensional collineation group. The planes of this family do not appear in the comprehensive classification [Betten, J. Reine Angew. Math. 285: 126–148, 1976, Betten, Geometriae Dedicata 3: 405–440, 1974/75, Betten, Math. Z. 154: 125–141, 1977]. We furthermore determine the isomorphism types of the new planes.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

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