Groups of Prime Power Order. / Volume 4 / / Yakov G. Berkovich, Zvonimir Janko.

• Superior document: Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
• VerfasserIn: Berkovich, Yakov G.,; Janko, Zvonimir,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2015]; ©2016
• Year of Publication: 2015
• Language: English
• Series: De Gruyter Expositions in Mathematics , 61
• Physical Description: 1 online resource (XVI, 459 p.)
• Other title: 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 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 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 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 --; Backmatter
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110281477; 9783110494969; 9783110762501; 9783110701005; 9783110439687; 9783110438765
• ISSN: 0938-6572
• DOI: 10.1515/9783110281477
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Yakov G. Berkovich, Zvonimir Janko.

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.