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Das Werk ist eine Einführung in die Charaktertheorie endlicher Gruppen, die zusammen mit der Darstellungstheorie einen wichtigen Bestandteil bei der Untersuchung der Struktur endlicher Gruppen bildet
List of contents
Notations and results from group theory; representations and representation-modules; simple and semisimple modules; orthogonality relations; the group algebra; characters of abelian groups; degrees of irreducible representations; characters of some small groups; products of representation and characters; on the number of solutions gm =1 in a group; a theorem of A. Hurwitz on multiplicative sums of squares ; permutation representations and characters; the class number; real characters and real representations; Coprime action; groups pa qb; Fronebius groups; induced characters; Brauer's permutation lemma and Glauberman's character correspondence; Clifford theory 1; projective representations; Clifford theory 2; extension of characters; Degree pattern and group structure; monomial groups; representation of wreath products; characters of p-groups; groups with a small number of character degrees; linear groups; the degree graph; groups all of whose character degrees are primes; two special degree problems; lengths of conjugacy classes; R. Brauer's theorem on the character ring; applications of Brauer's theorems; Artin's induction theorem; splitting fields; the Schur index; integral representations; three arithmetical applications; small kernels and faithful irreducible characters; TI-sets; involutions; groups whose Sylow-2-subgroups are generalized quaternion groups; perfect Fronebius complements. (Part contents).
Report
"Like every good textbook on the subject, it contains detailed treatments of the basics and the most important standard applications. [...] A distinctive feature of the book is the inclusion of many instructive examples, worked out with just the correct amount of detail. The reader encounters many groups and learns how to investigate them with the help of the theory previously developed. [...] It is needless to mention that this book once more proves the unequaled care and accuracy of its author." Mathematical Reviews
"[...] the reviewer found this "big blue" Huppert book a welcome enrichment of earlier books on character theory of finite groups." Zentralblatt für Mathematik
