Representations of Finite Groups
Characters, Maschke's theorem, and induced representations.
Representations of Finite Groups. Characters, Maschke’s theorem, and induced representations.
Foundations and canonical references
The standard treatments of representations of finite groups approach the subject from complementary angles. Serre, Linear Representations of Finite Groups (1977) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Isaacs, Character Theory of Finite Groups (1976) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for representations of finite groups include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1977Linear Representations of Finite Groupsserre-1977
- textbook · primary · 1976Character Theory of Finite Groupsisaacs-1976
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