Abstract.A reflection is an invertible linear transformation of a vector space fixing a given hyperplane, its axis, vectorwise and a given complement to this hyperplane, its center, setwise. A reflection torus is a onedimensional group generated by all reflections with fixed axis and center.In this paper we classify subgroups of general linear groups (in arbitrary dimension and defined over arbitrary fields) generated by reflection tori.
In this paper we study extended near hexagons, and classify a class of line systems in which two lines are either perpendicular, or make an angle α with cos α = ±1/3. Among the examples we encounter a set of 2300 lines in R 23 related to the second Conway group Co 2 and a set of 2048 lines in R 24 related to the group 2 1+11 :M 24 . The other line systems under consideration in this paper are all subsystems of these.MSC classification: 51E30, 05B99, 51E12, 20D8
Abstract. New technologies such as xml, xsl and both MathML and OpenMath make it possible to bring mathematics to the Internet. Indeed, OpenMath, a markup language for mathematical content, and OmDoc, its extension to mathematical documents, open a way of communicating mathematics between computers, between software applications and over the Internet without losing information. In this paper we describe the latest applications of OpenMath related technologies for Interactive Mathematical Documents. As an example we describe the way we incorporate these new technologies in a new version of Algebra Interactive, an interactive course on first and second year university algebra.
In this note we give two characterizations of the natural embedding of the classical G 2 L-hexagon in a projective space PV , where V is a 7-dimensional (or 6-dimensional in case the characteristic of L is 2) vector-space over an extension skew ®eld of L.We use these geometric results to characterize this vector-space V as a G 2 L-module on which the long root subgroups of G 2 L act quadratically with 2-dimensional commutator space.
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