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Groups of Prime Power Order, 2.
This is the second of three volumes devoted to elementary finite p-group theory. Similar to the first volume, hundreds of important results are analyzed and, in many cases, simplified. Important topics presented in this monograph include: (a) classification of p-groups all of whose cyclic subgroups...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
Walter de Gruyter,
2008.
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| Colección: | De Gruyter expositions in mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Frontmatter; Contents; List of definitions and notations; Preface; 46. Degrees of irreducible characters of Suzuki p-groups; 47. On the number of metacyclic epimorphic images of finite p-groups; 48. On 2-groups with small centralizer of an involution, I; 49. On 2-groups with small centralizer of an involution, II; 50. Janko's theorem on 2-groups without normal elementary abelian subgroups of order 8; 51. 2-groups with self centralizing subgroup isomorphic to E8; 52. 2-groups with 2-subgroup of small order; 53. 2-groups G with c2(G) = 4; 54. 2-groups G with cn(G) = 4, n>2.
- 55. 2-groups G with small subgroup (x? G
- o(x) = 2""); 56. Theorem of Ward on quaternion-free 2-groups; 57. Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4; 58. Non-Dedekindian p-groups all of whose nonnormal subgroups of the same order are conjugate; 59. p-groups with few nonnormal subgroups; 60. The structure of the Burnside group of order 212; 61. Groups of exponent 4 generated by three involutions; 62. Groups with large normal closures of nonnormal cyclic subgroups.
- 63. Groups all of whose cyclic subgroups of composite orders are normal; 64. p-groups generated by elements of given order; 65. A2-groups; 66. A new proof of Blackburn's theorem on minimal nonmetacyclic 2-groups; 67. Determination of U2-groups; 68. Characterization of groups of prime exponent; 69. Elementary proofs of some Blackburn's theorems; 70. Non-2-generator p-groups all of whose maximal subgroups are 2-generator; 71. Determination of A2-groups; 72. An-groups, n>2; 73. Classification of modular p-groups; 74. p-groups with a cyclic subgroup of index p2.
- 75. Elements of order = 4 in p-groups; 76. p-groups with few A1-subgroups; 77. 2-groups with a self-centralizing abelian subgroup of type (4, 2); 78. Minimal nonmodular p-groups; 79. Nonmodular quaternion-free 2-groups; 80. Minimal non-quaternion-free 2-groups; 81. Maximal abelian subgroups in 2-groups; 82. A classification of 2-groups with exactly three involutions; 83. p-groups G with O2(G) or O2*(G) extraspecial; 84. 2-groups whose nonmetacyclic subgroups are generated by involutions; 85. 2-groups with a nonabelian Frattini subgroup of order 16.
- 86. p-groups G with metacyclic O2*(G); 87. 2-groups with exactly one nonmetacyclic maximal subgroup; 88. Hall chains in normal subgroups of p-groups; 89. 2-groups with exactly six cyclic subgroups of order 4; 90. Nonabelian 2-groups all of whose minimal nonabelian subgroups are of order 8; 91. Maximal abelian subgroups of p-groups; 92. On minimal nonabelian subgroups of p-groups; Appendix 16. Some central products; Appendix 17. Alternate proofs of characterization theorems of Miller and Janko on 2-groups, and some related results; Appendix 18. Replacement theorems.