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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Berkovich, Yakov
Otros Autores: Janko, Zvonimir
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin : Walter de Gruyter, 2008.
Colección:De Gruyter expositions in mathematics.
Temas:
Finite groups.
Group theory.
Groupes finis.
Théorie des groupes.
Finite groups
Group theory
Acceso en línea:Texto completo

MARC

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100 1 |a Berkovich, Yakov. 
245 1 0 |a Groups of Prime Power Order, 2. 
260 |a Berlin :  |b Walter de Gruyter,  |c 2008. 
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490 1 |a De Gruyter Expositions in Mathematics 
520 |a 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 of composite orders are normal, (b) classification of 2-groups with exactly three involutions, (c) two proofs of Ward's theorem on quaternion-free groups, (d) 2-groups with small centralizers of an involution, (e) classification of 2-groups with exactly four cyclic subgroups of order 2n & 2, (f) two. 
588 0 |a Print version record. 
505 0 |a 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. 
505 8 |a 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. 
505 8 |a 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. 
505 8 |a 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. 
505 8 |a 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. 
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650 0 |a Finite groups. 
650 0 |a Group theory. 
650 6 |a Groupes finis. 
650 6 |a Théorie des groupes. 
650 7 |a Finite groups  |2 fast 
650 7 |a Group theory  |2 fast 
700 1 |a Janko, Zvonimir. 
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