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Linear Groups

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Algebra IV

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 37))

Abstract

It is hardly necessary to expatiate here on the widespread and manifold applications of group theory. For all that, it must be emphasised that applications are always associated with realisations of groups as groups of transformations (essentially, that is, as groups of symmetries) of some mathematical system or other. Without doubt, the most important types of transformation groups are the groups of linear transformations, that is, the linear groups. Their significance in the natural sciences was appreciated at the very dawn of the development of group theory. One of the earliest and most impressive instances of this is the classification of crystallographic groups (1890).

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  1. A. E. Zalesskij
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  1. Steklov Mathematical Institute, ul. Vavilova 42, 117966, Moscow, Russia

    A. I. Kostrikin  & I. R. Shafarevich  & 

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Zalesskij, A.E. (1993). Linear Groups. In: Kostrikin, A.I., Shafarevich, I.R. (eds) Algebra IV. Encyclopaedia of Mathematical Sciences, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02869-8_2

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  • DOI: https://doi.org/10.1007/978-3-662-02869-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08100-2

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