Abstract
In this chapter we consider groups whose generators are involutory while their products in pairs have assigned periods; we ask especially what values of the periods will make such a group finite. Cases where the number of generators is less than four have been considered in 4.31 and 4.32. We shall prove that the generators may always be represented by real affine reflections, thus preparing the ground for a complete enumeration of the finite groups. Then we shall describe some of their remarkable properties.
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© 1957 Springer-Verlag Berlin Heidelberg
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Coxeter, H.S.M., Moser, W.O.J. (1957). Groups Generated by Reflections. In: Generators and Relations for Discrete Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25739-5_9
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DOI: https://doi.org/10.1007/978-3-662-25739-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-23654-3
Online ISBN: 978-3-662-25739-5
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