Some applications of representation theory

  • W. Plesken
Chapter
Part of the Progress in Mathematics book series (PM, volume 95)

Abstract

Group representation theory has grown out of group theory. Therefore one way of measuring progress is by looking at the applications of representation theory to group theory and theories where groups play a role. In this note I discuss two areas of applications, which I have been involved in. A third area, which is left out here, is that of extensions. As pointed out in [HoP 89] representation theory not only provides abelian normal subgroups for extensions with given factor group, but also nonabelian (e.g. pro-p) normal subgroups. A fourth area, which I also only mention in passing, is that of applications to computational group theory, more precisely to the investigation of finite presentations of groups, cf. [Ple 87], [HoP 89] Chapter 7, [HoP 90].

Keywords

Normal Subgroup Finite Group Conjugacy Class Representation Theory Point Group 
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© Springer Basel AG 1991

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  • W. Plesken

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