Groups of Prime Power Order Volume 4 /
This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawas theorem on p-groups with two size...
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston :
De Gruyter,
[2015]
|
| Series: | De Gruyter expositions in mathematics
61 |
| Subjects: |
Table of Contents:
- Frontmatter
- Contents
- List of definitions and notations
- Preface
- § 145 p-groups all of whose maximal subgroups, except one, have derived subgroup of order ≤ p
- § 146 p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups
- § 147 p-groups with exactly two sizes of conjugate classes
- § 148 Maximal abelian and minimal nonabelian subgroups of some finite two-generator p-groups especially metacyclic
- § 149 p-groups with many minimal nonabelian subgroups
- § 150 The exponents of finite p-groups and their automorphism groups
- § 151 p-groups all of whose nonabelian maximal subgroups have the largest possible center
- § 152 p-central p-groups
- § 153 Some generalizations of 2-central 2-groups
- § 154 Metacyclic p-groups covered by minimal nonabelian subgroups
- § 155 A new type of Thompson subgroup
- § 156 Minimal number of generators of a p-group, p 2
- § 157 Some further properties of p-central p-groups
- § 158 On extraspecial normal subgroups of p-groups
- § 159 2-groups all of whose cyclic subgroups A, B with A ∩ B ≠ {1} generate an abelian subgroup
- § 160 p-groups, p 2, all of whose cyclic subgroups A, B with A ∩ B ≠ {1} generate an abelian subgroup
- § 161 p-groups where all subgroups not contained in the Frattini subgroup are quasinormal
- § 162 The centralizer equality subgroup in a p-group
- § 163 Macdonalds theorem on p-groups all of whose proper subgroups are of class at most 2
- § 164 Partitions and Hp-subgroups of a p-group
- § 165 p-groups G all of whose subgroups containing Φ(G) as a subgroup of index p are minimal nonabelian
- § 166 A characterization of p-groups of class 2 all of whose proper subgroups are of class ≤ 2
- § 167 Nonabelian p-groups all of whose nonabelian subgroups contain the Frattini subgroup
- § 168 p-groups with given intersections of certain subgroups
- § 169 Nonabelian p-groups G with 〈A, B〉 minimal nonabelian for any two distinct maximal cyclic subgroups A, B of G
- § 170 p-groups with many minimal nonabelian subgroups, 2
- § 171 Characterizations of Dedekindian 2-groups
- § 172 On 2-groups with small centralizers of elements
- § 173 Nonabelian p-groups with exactly one noncyclic maximal abelian subgroup
- § 174 Classification of p-groups all of whose nonnormal subgroups are cyclic or abelian of type (p, p)
- § 175 Classification of p-groups all of whose nonnormal subgroups are cyclic, abelian of type (p, p) or ordinary quaternion
- § 176 Classification of p-groups with a cyclic intersection of any two distinct conjugate subgroups
- § 177 On the norm of a p-group
- § 178 p-groups whose character tables are strongly equivalent to character tables of metacyclic p-groups, and some related topics
- § 179 p-groups with the same numbers of subgroups of small indices and orders as in a metacyclic p-group
- § 180 p-groups all of whose noncyclic abelian subgroups are normal
- § 181 p-groups all of whose nonnormal abelian subgroups lie in the center of their normalizers
- § 182 p-groups with a special maximal cyclic subgroup
- § 183 p-groups generated by any two distinct maximal abelian subgroups
- § 184 p-groups in which the intersection of any two distinct conjugate subgroups is cyclic or generalized quaternion
- § 185 2-groups in which the intersection of any two distinct conjugate subgroups is either cyclic or of maximal class
- § 186 p-groups in which the intersection of any two distinct conjugate subgroups is either cyclic or abelian of type (p, p)
- § 187 p-groups in which the intersection of any two distinct conjugate cyclic subgroups is trivial
- § 188 p-groups with small subgroups generated by two conjugate elements
- § 189 2-groups with index of every cyclic subgroup in its normal closure ≤ 4
- Appendix 45 Varia II
- Appendix 46 On Zsigmondy primes
- Appendix 47 The holomorph of a cyclic 2-group
- Appendix 48 Some results of R. van der Waall and close to them
- Appendix 49 Kegels theorem on nilpotence of Hp-groups
- Appendix 50 Sufficient conditions for 2-nilpotence
- Appendix 51 Varia III
- Appendix 52 Normal complements for nilpotent Hall subgroups
- Appendix 53 p-groups with large abelian subgroups and some related results
- Appendix 54 On Passmans Theorem 1.25 for p 2
- Appendix 55 On p-groups with the cyclic derived subgroup of index p2
- Appendix 56 On finite groups all of whose p-subgroups of small orders are normal
- Appendix 57 p-groups with a 2-uniserial subgroup of order p and an abelian subgroup of type (p, p)
- Research problems and themes IV
- Bibliography
- Author index
- Subject index
- Backmatter