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- catalog alternative "Teorii︠a︡ kharakterov. English".
- catalog contributor b10709495.
- catalog contributor b10709496.
- catalog contributor b10709497.
- catalog created "c1998-c1999.".
- catalog date "1998".
- catalog date "c1998-c1999.".
- catalog dateCopyrighted "c1998-c1999.".
- catalog description "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.".
- catalog description "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.".
- catalog description "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.".
- catalog description "Includes bibliographical references (pt. 1, p. 361-375) and indexes.".
- catalog description "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 --".
- catalog description "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.".
- catalog extent "2 v. ;".
- catalog identifier "082184606X (pt. 1 : acid-free paper)".
- catalog isPartOf "Translations of mathematical monographs ; v. 172, v. 181".
- catalog issued "1998".
- catalog issued "c1998-c1999.".
- catalog language "eng rus".
- catalog language "eng".
- catalog publisher "Providence, R.I. : American Mathematical Society,".
- catalog subject "Characters of groups.".
- catalog subject "Finite groups.".
- catalog subject "QA177 .B4713 1998".
- catalog tableOfContents "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.".
- catalog tableOfContents "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.".
- catalog tableOfContents "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.".
- catalog tableOfContents "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 --".
- catalog tableOfContents "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.".
- catalog title "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].".
- catalog title "Teorii︠a︡ kharakterov. English".
- catalog type "text".