Groups of Prime Power Order: Volume 3 (De Gruyter Expositions in Mathematics)

Groups of Prime Power Order - Volume 3\r......Page 1
De Gruyter Expositions in Mathematics 56......Page 2
ISBN: 9783110207170......Page 5
--> Contents......Page 6
List of definitions and notations......Page 10
Preface......Page 16
Prerequisites from Volumes 1 and 2......Page 18
§ 93 - Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4......Page 28
§ 94 - Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4......Page 35
§ 95 - Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e......Page 37
§ 96 - Groups with at most two conjugate classes of nonnormal subgroups......Page 39
§ 97 - p-groups in which some subgroups are generated by elements of order p......Page 51
§ 98 - Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2nC1, n  > 3 fixed......Page 58
§ 99 - 2-groups with sectional rank at most 4......Page 61
§ 100 - 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian......Page 73
§ 102 - p-groups G with p > 2 and d. (G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian......Page 93
§ 101 - p-groups G with p > 2 and d (G) =  2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian......Page 109
§ 103 - Some results of Jonah and Konvisser......Page 120
§ 104 - Degrees of irreducible characters of p-groups associated with finite algebras......Page 124
§ 105 - On some special p-groups......Page 129
§ 106 - On maximal subgroups of two-generator 2-groups......Page 137
§ 107 - Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups......Page 140
§ 108 - p-groups with few conjugate classes of minimal nonabelian subgroups......Page 147
§ 109 - On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p......Page 149
§ 110 - Equilibrated p-groups......Page 152
§ 111 - Characterization of abelian and minimal nonabelian groups......Page 161
§ 112 - Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order......Page 167
§ 113 - The class of 2-groups in § 70 is not bounded......Page 175
§ 114 - Further counting theorems......Page 179
§ 115 - Finite p-groups all of whose maximal subgroups except one are extraspecial......Page 184
§ 116 - Groups covered by few proper subgroups......Page 189
§ 117 - 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class......Page 203
§ 118 - Review of characterizations of p-groups with various minimal nonabelian subgroups......Page 206
§ 119 - Review of characterizations of p-groups of maximal class......Page 212
§ 120 - Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection......Page 219
§ 121 - p-groups of breadth 2......Page 224
§ 122 - p-groups all of whose subgroups have normalizers of index at most p......Page 231
§ 123 - Subgroups of finite groups generated by all elements in two shortest conjugacy classes......Page 264
§ 124 - The number of subgroups of given order in a metacyclic p-group......Page 266
§ 125 - p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant......Page 296
§ 126 - The existence of p-groups G1 < G such that Aut (G1) = Aut (G)......Page 299
§ 127 - On 2-groups containing a maximal elementary abelian subgroup of order 4......Page 302
§ 128 - The commutator subgroup of p-groups with the subgroup breadth 1......Page 304
§ 129 - On two-generator 2-groups with exactly one maximal subgroup which is not two-generator......Page 312
§ 130 - Soft subgroups of p-groups......Page 314
§ 131 - p-groups with a 2-uniserial subgroup of order p......Page 319
§ 132 - On centralizers of elements in p-groups......Page 322
§ 133 - Class and breadth of a p-group......Page 327
§ 134 - On p-groups with maximal elementary abelian subgroup of order p2......Page 331
§ 135 - Finite p-groups generated by certain minimal nonabelian subgroups......Page 342
§ 136 - p-groups in which certain proper nonabelian subgroups are two-generator......Page 355
§ 137 - p-groups all of whose proper subgroups have its derived subgroup of order at most p......Page 365
§ 138 - p-groups all of whose nonnormal subgroups have the smallest possible normalizer......Page 370
§ 139 - p-groups with a noncyclic commutator group all of whose proper subgroups have a cyclic commutator group......Page 382
§ 140 - Power automorphisms and the norm of a p-group......Page 390
§ 141 - Nonabelian p-groups having exactly one maximal subgroup with a noncyclic center......Page 395
§ 142 - Nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal nonabelian......Page 397
§ 143 - Alternate proof of the Reinhold Baer theorem on 2-groups with nonabelian norm......Page 400
§ 144 - p-groups with small normal closures of all cyclic subgroups......Page 403
Appendix 27 - Wreathed 2-groups......Page 411
Appendix 28 - Nilpotent subgroups......Page 420
Appendix 29 - Intersections of subgroups......Page 432
Appendix 30 - Thompson’s lemmas......Page 443
Appendix 31 - Nilpotent p\'-subgroups of class 2 in GL (n; p)......Page 455
Appendix 32 - On abelian subgroups of given exponent and small index......Page 461
Appendix 33 - On Hadamard 2-groups......Page 464
Appendix 34 - Isaacs–Passman’s theorem on character degrees......Page 467
Appendix 35 - Groups of Frattini class 2......Page 473
Appendix 36 - Hurwitz’ theorem on the composition of quadratic forms......Page 476
Appendix 37 - On generalized Dedekindian groups......Page 479
Appendix 38 - Some results of Blackburn and Macdonald......Page 484
Appendix 39 - Some consequences of Frobenius’ normal p-complement theorem......Page 487
Appendix 40 - Varia......Page 499
Appendix 41 - Nonabelian 2-groups all of whose minimal nonabelian subgroups have cyclic centralizers......Page 541
Appendix 42 - On lattice isomorphisms of p-groups of maximal class......Page 543
Appendix 43 - Alternate proofs of two classical theorems on solvable groups and some related results......Page 546
Appendix 44 - Some of Freiman’s results on finite subsets of groups with small doubling......Page 554
Research problems and themes III......Page 563
Bibliography......Page 620
Author index......Page 657
Subject index......Page 659