Characters of Finite Groups. Part 1

Description

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 Content: 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.