- 巻冊次
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pt. 2 ISBN 9780821805329
内容説明
This book places character theory and its applications to finite groups within the reach of people with a comparatively modest mathematical background. The work concentrates mostly on applications of character theory to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups. The presentation is detailed, and many proofs of known results are new.
目次
Degrees and kernels of irreducible characters Involutions Connectedness and Zassenhaus groups The Nagao theorem Linear groups Permutation characters Characters of SL$(2,p^n)$ Zeros of characters The Schur index On degrees of irreducible components of induced characters Groups in which only two nonlinear irreducible characters have equal degrees Groups with small sums of degrees of some characters On sums of degrees of irreducible characters Groups whose nonlinear irreducible characters take three distinct values Nonsolvable groups with many involutions On kernels of nonlinear irreducible characters On monolithic characters The class number Problems Notes on the bibliography Bibliography Author index Subject index List of corrections to part 1.
- 巻冊次
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pt. 1 ISBN 9780821846063
内容説明
This book discusses character theory and its applications to finite groups. The work places the subject within the reach of people with a relatively modest mathematical background. The necessary background exceeds the standard algebra course with respect only to finite groups. Starting with basic notions and theorems in character theory, the authors present a variety of results on the properties of complex-valued characters and applications to finite groups.The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations and applications of monomial groups. The presentation is detailed, and many proofs of known results are new. Most of the results in the book are presented in monograph form for the first time. Numerous exercises offer additional information on the topics and help readers to understand the main concepts and results.
目次
Basic concepts Characters On arithmetical properties of characters Products of characters Induced characters and representations Projective representations Clifford theory Brauer's induction theorems Faithful representations Existence of normal subgroups On sums of degrees of irreducible characters Groups of relatively small height The Brauer-Suzuki theorem Appendices Notes on the bibliography Bibliography Author index Subject index.
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