Groups of Prime Power Order. Volume 4

Name: Groups of Prime Power Order. Volume 4 | Volume 4
Brand: De Gruyter
Price: 230.0 EUR
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Volume 4

Yakov G. Berkovich Zvonimir Janko(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 14. Dezember 2015

XVI, 459 Seiten

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978-3-11-028147-7 (ISBN)

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Beschreibung

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
Ishikawa's theorem on p- groups with two sizes of conjugate classes
p- central p- groups
theorem of Kegel on nilpotence of H p -groups
partitions of p- groups
characterizations of Dedekindian groups
norm of p- groups
p- groups with 2-uniserial subgroups of small order

The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra.

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Inhalt

Intro
Content
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 Macdonald's 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 ØG) 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 Kegel's 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 Passman's 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

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