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Some Ideas in the Classification of the Finite Simple Groups

In: Algebra, Arithmetic and Geometry with Applications

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  • Gernot Stroth

Abstract

Everything we report about is joint work with U. Meierfrankenfeld and B. Stellmacher. The key idea for the existing classification of the finite simple groups is due R. Brauer [Br],[BrFo]. He suggested to classify the finite simple groups by the centralizers of their involutions. On the first view this does not look very promissing, as the property of a group H to act as a centralizer of an involution is just to have an element of order two in Z(H). So there are as many centralizers as groups. But on the other hand the classification went this road. Of course one had to find ways to reduce the possible structures of centralizers. We will look at the following generalization.

Suggested Citation

  • Gernot Stroth, 2004. "Some Ideas in the Classification of the Finite Simple Groups," Springer Books, in: Chris Christensen & Avinash Sathaye & Ganesh Sundaram & Chandrajit Bajaj (ed.), Algebra, Arithmetic and Geometry with Applications, pages 725-731, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18487-1_43
    DOI: 10.1007/978-3-642-18487-1_43
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