Character theory of finite groups

著者

• Huppert, B. (Bertram)

書誌事項

Character theory of finite groups

by Bertram Huppert

（De Gruyter expositions in mathematics, 25）

Walter de Gruyter, 1998

注記

Includes bibliographical references and indexes

内容説明・目次

内容説明

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Aix-Marseille Universite, France Katrin Wendland, Trinity College Dublin, Dublin, Ireland Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

目次

• 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).

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詳細情報

• NII書誌ID(NCID): BA37192354
• ISBN:
  • 9783110154214
• LCCN: 98008805
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin ; New York
• ページ数/冊数: vi, 618 p.
• 分類:
  • LCC : QA177
  • DC21 : 512/.2
• 件名:
  • LCSH : Finite groups
  • LCSH : Characters of groups
• 親書誌ID:
  • BA10903360