Research Article

Polar Kangaroos of Type E₆

Published in: Quaestiones Mathematicae
Volume 49 , issue 3 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 307–333

DOI: 10.2989/16073606.2025.2581625

Author(s): Yannick Neyt Ghent University, Belgium, Hendrik Van Maldeghem Ghent University, Belgium,

Keywords: 51E24, Spherical buildings, long root subgroup geometry, displacement spectrum, Groups of type E6,

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Abstract

A collineation of a point-line geometry is called a kangaroo if its displacement spectrum has a gap; that is, at least one certain distance smaller than the diameter of the geometry cannot occur between a point and its image. In this paper we consider kangaroos in the exceptional long root subgroup geometry of type E₆ over an arbitrary field and classify them.

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