Groups of Prime Power Order. Volume 2 (eBook)

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Yakov Berkovich, University of Haifa, Israel; Zvonimir Janko, Universität Heidelberg.

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

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