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Linear Groups Generated by Reflection Tori

Published online by Cambridge University Press:  20 November 2018

A. M. Cohen ,
H. Cuypers  and
H. Sterk
A. M. Cohen
Affiliation:
Department of Mathematics, Eindhoven University of Technology, P.O. BOX 513, 5600 MB Eindhoven, The Netherlands
H. Cuypers
Affiliation:
Department of Mathematics, Eindhoven University of Technology, P.O. BOX 513, 5600 MB Eindhoven, The Netherlands
H. Sterk
Affiliation:
Department of Mathematics, Eindhoven University of Technology, P.O. BOX 513, 5600 MB Eindhoven, The Netherlands
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Abstract

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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 one-dimensional 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.

Keywords

20Hxx20Gxx51A50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 6 , 01 December 1999 , pp. 1149 - 1174
Copyright
Copyright © Canadian Mathematical Society 1999

References

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