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" Characters of finite groups / "
Ya. G. Berkovich, E.M. Zhmudʹ ; [translated by P. Shumyatsky and V. Zobina from the original Russian manuscript ; translation edited by David Louvish].
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BL
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637223
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dltt
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TeoriiÍŁa kharakterov.English
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| Main Entry
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Berkovich, IÍŁA. G.,1938-
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| Title & Author
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Characters of finite groups /\ Ya. G. Berkovich, E.M. Zhmudʹ ; [translated by P. Shumyatsky and V. Zobina from the original Russian manuscript ; translation edited by David Louvish].
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| Publication Statement
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Providence, R.I. :: American Mathematical Society,, c1998-1999.
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| Series Statement
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Translations of mathematical monographs ;; v. 172, 181
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2 v. ;; 26 cm.
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| ISBN
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082184606X (pt. 1 : acid-free paper)
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: 9780821846063 (pt. 1 : acid-free paper)
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: 0821805320 (pt. 2 : acid-free paper)
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: 9780821805329 (pt. 2 : acid-free paper)
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| Bibliographies/Indexes
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Includes bibliographical references and indexes.
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| Contents
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Chapter 14 Degrees and Kernels of Irreducible Characters 1 -- 1. Garrison's Theorems 1 -- 2. Theorems of Blichfeldt and Isaacs-Passman 6 -- 3. Thompson's Theorem on degrees 11 -- 4. Groups with irreducible characters of small degrees 13 -- 5. A [pi]-nilpotency criterion 14 -- 6. Gallagher's Theorem 15 -- 7. Isaacs' Three Character Degrees Theorem 16 -- 8. Solvability of a group G such that cd G is almost a chain 17 -- 9. On intersections of kernels of some characters 20 -- 10. The Chillag-Herzog Theorem 23 -- 11. Isaacs' Theorem 25 -- 12. The degree graph 26 -- 13. On quasikernels of irreducible characters 28 -- 14. A nilpotency criterion 29 -- 15. Minkowski's Theorem 30 -- 16. A [pi]-closure criterion 32 -- 17. Generalizations of M-groups 34 -- Appendix A. On Taketa's Theorem 38 -- Appendix B. On Isaacs' solvability criterion 46 -- Appendix C. An excursion into group theory 50 -- Chapter 15. Involutions 59 -- 1. Groups of even order contain large subgroups 60 -- 2. Groups with two nonconjugate involutions 66 -- 3. Real elements 69 -- 4. Applications to characters 76 -- 5. Bender's method 77 -- 6. Brauer's and Thompson's formulas 82 -- Chapter 16. Connectedness and Zassenhaus Groups 85 -- 1. Veitsblit's Theorem 85 -- 2. Proof of Theorem 1 86 -- 3. On Thompson's question 93 -- 4. Suzuki's Theorems on ZT-groups 94 -- 5. Characterization of Zassenhaus groups 94 -- Chapter 17. The Nagao Theorem 99 -- Chapter 18. Linear Groups 105 -- 1. Linear groups of small degree 105 -- 2. Jordan's Theorem 108 -- Chapter 19. Permutation Characters 113 -- 1. The number of orbits 113 -- 2. The character of the direct product of two actions 114 -- 3. Bell numbers and powers of the natural character 114 -- 4. On characters of m-transitive permutation groups 117 -- 5. On 4-transitive permutation groups 123 -- 6. The character table of S[subscript 5] 124 -- 7. The character table of S[subscript 6] 125 -- 8. The minimal degree of a faithful character of S[subscript n] 127 -- 9. Introduction to Young theory 128 -- Chapter 20. Characters of SL(2, p[superscript n]) 137 -- 1. Classes of G when p is odd 137 -- 2. Character table of G when p is odd 140 -- 3. The case p = 2 143 -- Chapter 21. Zeros of Characters 145 -- 1. General facts 145 -- 2. Groups with x-maximal subgroup. S-characters 154 -- Chapter 22. The Schur Index 165 -- Chapter 23. On Degrees of Irreducible Components of Induced Characters 181 -- Chapter 24. Groups in Which Only Two Nonlinear Irreducible Characters Have Equal Degrees 189 -- 2. Nilpotent D[subscript 1]-groups 190 -- 3. Key lemma 191 -- 4. Metabelian D[subscript 1]-groups 192 -- 5. Proof of the main theorem 195 -- Chapter 25. Groups with Small Sums of Degrees of Some Characters 203 -- 1. Auxiliary results 203 -- 2. The first main theorem 208 -- 3. The second main theorem 209 -- 4. Groups with cyclic Sylow p-subgroups 210 -- Appendix A generalization of Frobenius kernels 214 -- Chapter 26. On Sums of Degrees of Irreducible Characters 219 -- 2. Pairs H < G with [delta subscript 0](G, H) = 1 220 -- 3. Pairs H < G with [delta subscript 0](G, H) = 2 222 -- 4. p-groups 230 -- Chapter 27. Groups Whose Nonlinear Irreducible Characters Take Three Values 233 -- 1. Statement of the main theorem 233 -- 2. Preliminaries 233 -- 3. Proof of the main theorem 236 -- 4. A 4-values analog to Lemma 2 239 -- Chapter 28. Nonsolvable Groups with Many Involutions 243 -- Chapter 29. On Kernels of Nonlinear Irreducible Characters 249 -- Chapter 30. On Monolithic Characters 255 -- 2. Proof of the Main Theorem 257 -- 3. A generalization of CM-groups 261 -- 4. Generalizations of Thompson's and Michler's Theorems 263 -- Appendix A. On Isaacs' Three Character Degrees Theorem 265 -- Appendix B. On Zsigmondy primes 271 -- Chapter 31. The Class Number 277 -- 1. On the class number of a p-group 277 -- 2. Landau's Theorem 278 -- 3. The elements of Irr[subscript 1] (G) are algebraically conjugate 279 -- 4. Groups with two nonlinear irreducible characters 281 -- 5. Groups with three nonlinear irreducible characters 281 -- 6. The minimal number of generators and the class number 285 -- 7. p-groups with few nonlinear irreducible characters 286 -- 8. Isaacs-Passman's Theorems 287 -- 9. Lin(G) acts on Irr[subscript 1](G) transitively 289.
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| Subject
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Finite groups.
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| Subject
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Characters of groups.
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| LC Classification
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QA177.B4713 1998
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| Added Entry
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Zhmudʣ, E. M.,1918-
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Louvish, David.
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