Berkovich / Janko Groups of Prime Power Order

Volume 2
1. Auflage 2008
ISBN: 978-3-11-020823-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 2, 611 Seiten

Reihe: Groups of Prime Power Order

Zielgruppe

Researchers, Graduate Students of Mathematics; Academic Libraries

Autoren/Hrsg.

Berkovich, Yakov

Janko, Zvonimir

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

1;Frontmatter;1
2;Contents;5
3;List of definitions and notations;8
4;Preface;14
5;§46. Degrees of irreducible characters of Suzuki p-groups;17
6;§47. On the number of metacyclic epimorphic images of finite p-groups;30
7;§48. On 2-groups with small centralizer of an involution, I;35
8;§49. On 2-groups with small centralizer of an involution, II;44
9;§50. Janko’s theorem on 2-groups without normal elementary abelian subgroups of order 8;59
10;§51. 2-groups with self centralizing subgroup isomorphic to E8;68
11;§52. 2-groups with 2-subgroup of small order;91
12;§53. 2-groups G with c2(G) = 4;112
13;§54. 2-groups G with cn(G) = 4, n > 2;125
14;§55. 2-groups G with small subgroup (x . G | o(x) = 2");138
15;§56. Theorem of Ward on quaternion-free 2-groups;150
16;§57. Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4;156
17;§58. Non-Dedekindian p-groups all of whose nonnormal subgroups of the same order are conjugate;163
18;§59. p-groups with few nonnormal subgroups;166
19;§60. The structure of the Burnside group of order 212;167
20;§61. Groups of exponent 4 generated by three involutions;179
21;§62. Groups with large normal closures of nonnormal cyclic subgroups;185
22;§63. Groups all of whose cyclic subgroups of composite orders are normal;188
23;§64. p-groups generated by elements of given order;195
24;§65. A2-groups;204
25;§66. A new proof of Blackburn’s theorem on minimal nonmetacyclic 2-groups;213
26;§67. Determination of U2-groups;218
27;§68. Characterization of groups of prime exponent;222
28;§69. Elementary proofs of some Blackburn’s theorems;225
29;§70. Non-2-generator p-groups all of whose maximal subgroups are 2-generator;230
30;§71. Determination of A2-groups;249
31;§72. An-groups, n > 2;264
32;§73. Classification of modular p-groups;273
33;§74. p-groups with a cyclic subgroup of index p2;290
34;§75. Elements of order = 4 in p-groups;293
35;§76. p-groups with few A1-subgroups;298
36;§77. 2-groups with a self-centralizing abelian subgroup of type (4, 2);332
37;§78. Minimal nonmodular p-groups;339
38;§79. Nonmodular quaternion-free 2-groups;350
39;§80. Minimal non-quaternion-free 2-groups;372
40;§81. Maximal abelian subgroups in 2-groups;377
41;§82. A classification of 2-groups with exactly three involutions;384
42;§83. p-groups G with O2(G) or O2*(G) extraspecial;412
43;§84. 2-groups whose nonmetacyclic subgroups are generated by involutions;415
44;§85. 2-groups with a nonabelian Frattini subgroup of order 16;418
45;§86. p-groups G with metacyclic O2*(G);422
46;§87. 2-groups with exactly one nonmetacyclic maximal subgroup;428
47;§88. Hall chains in normal subgroups of p-groups;453
48;§89. 2-groups with exactly six cyclic subgroups of order 4;470
49;§90. Nonabelian 2-groups all of whose minimal nonabelian subgroups are of order 8;479
50;§91. Maximal abelian subgroups of p-groups;483
51;§92. On minimal nonabelian subgroups of p-groups;490
52;Appendix 16. Some central products;501
53;Appendix 17. Alternate proofs of characterization theorems of Miller and Janko on 2-groups, and some related results;508
54;Appendix 18. Replacement theorems;517
55;Appendix 19. New proof of Ward’s theorem on quaternion-free 2-groups;522
56;Appendix 20. Some remarks on automorphisms;525
57;Appendix 21. Isaacs’ examples;528
58;Appendix 22. Minimal nonnilpotent groups;532
59;Appendix 23. Groups all of whose noncentral conjugacy classes have the same size;535
60;Appendix 24. On modular 2-groups;538
61;Appendix 25. Schreier’s inequality for p-groups;542
62;Appendix 26. p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class;545
63;Research problems and themes II;547
64;Backmatter;585

Über Autor(innen)

Janko, Zvonimir
Zvonimir Janko, Universität Heidelberg

Berkovich, Yakov
Yakov Berkovich, University of Haifa, Israel

Yakov Berkovich, University of Haifa, Israel;

Zvonimir Janko, Universität Heidelberg