Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order, Volume 2

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Walter de Gruyter, Dec 10, 2008 - Mathematics - 611 pages
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This is the second of three volumes on finite p-group theory, written by two prominent authors in the area.

 

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Contents

77 2groups with a selfcentralizing abelian subgroup of type 4 2
316
78 Minimal nonmodular pgroups
323
79 Nonmodular quaternionfree 2groups
334
80 Minimal nonquaternionfree 2groups
356
81 Maximal abelian subgroups in 2groups
361
82 A classification of 2groups with exactly three involutions
368
83 pgroups G with Ω2G or Ω2G extraspecial
396
84 2groups whose nonmetacyclic subgroups are generated by involutions
399

54 2groups G with cnG 4 n 2
109
55 2groups G with small subgroup x G ox 2
122
56 Theorem of Ward on quaternionfree 2groups
134
57 Nonabelian 2groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4
140
58 NonDedekindian pgroups all of whose nonnormal subgroups of the same order are conjugate
147
59 pgroups with few nonnormal subgroups
150
60 The structure of the Burnside group of order 212
151
61 Groups of exponent 4 generated by three involutions
163
62 Groups with large normal closures of nonnormal cyclic subgroups
169
63 Groups all of whose cyclic subgroups of composite orders are normal
172
64 pgroups generated by elements of given order
179
65 A2groups
188
66 A new proof of Blackburns theorem on minimal nonmetacyclic 2groups
197
67 Determination of U2groups
202
68 Characterization of groups of prime exponent
206
69 Elementary proofs of some Blackburns theorems
209
70 Non2generator pgroups all of whose maximal subgroups are 2generator
214
71 Determination of A2groups
233
72 Angroups n 2
248
73 Classification of modular pgroups
257
74 pgroups with a cyclic subgroup of index p2
274
75 Elements of order 4 in pgroups
277
76 pgroups with few A1subgroups
282
85 2groups with a nonabelian Frattini subgroup of order 16
402
86 pgroups G with metacyclic Ω2G
406
87 2groups with exactly one nonmetacyclic maximal subgroup
412
88 Hall chains in normal subgroups of pgroups
437
89 2groups with exactly six cyclic subgroups of order 4
454
90 Nonabelian 2groups all of whose minimal nonabelian subgroups are of order 8
463
91 Maximal abelian subgroups of pgroups
467
92 On minimal nonabelian subgroups of pgroups
474
Appendix 16 Some central products
485
Appendix 17 Alternate proofs of characterization theorems of Miller and Janko on 2groups and some related results
492
Appendix 18 Replacement theorems
501
Appendix 19 New proof of Wards theorem on quaternionfree 2groups
506
Appendix 20 Some remarks on automorphisms
509
Appendix 21 Isaacs examples
512
Appendix 22 Minimal nonnilpotent groups
516
Appendix 23 Groups all of whose noncentral conjugacy classes have the same size
519
Appendix 24 On modular 2groups
522
Appendix 25 Schreiers inequality for pgroups
526
Appendix 26 pgroups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class
529
Research problems and themes II
531
Backmatter
569
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About the author (2008)

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

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