Some Ideas in the Classification of the Finite Simple Groups

Gernot Stroth

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 725-731 from Springer

Abstract: 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.

Keywords: Automorphism Group; Simple Group; Maximal Subgroup; Wreath Product; Structure Theorem (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_43

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DOI: 10.1007/978-3-642-18487-1_43

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