UID:
almafu_9959237949102883
Format:
1 online resource (476 p.)
ISBN:
3-11-028147-3
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3-11-038155-9
Series Statement:
De Gruyter Expositions in Mathematics, Volume 61
Content:
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.
Note:
Description based upon print version of record.
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Frontmatter --
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Contents --
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List of definitions and notations --
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Preface --
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§ 145 p-groups all of whose maximal subgroups, except one, have derived subgroup of order ≤ p --
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§ 146 p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups --
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§ 147 p-groups with exactly two sizes of conjugate classes --
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§ 148 Maximal abelian and minimal nonabelian subgroups of some finite two-generator p-groups especially metacyclic --
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§ 149 p-groups with many minimal nonabelian subgroups --
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§ 150 The exponents of finite p-groups and their automorphism groups --
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§ 151 p-groups all of whose nonabelian maximal subgroups have the largest possible center --
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§ 152 p-central p-groups --
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§ 153 Some generalizations of 2-central 2-groups --
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§ 154 Metacyclic p-groups covered by minimal nonabelian subgroups --
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§ 155 A new type of Thompson subgroup --
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§ 156 Minimal number of generators of a p-group, p 〉 2 --
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§ 157 Some further properties of p-central p-groups --
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§ 158 On extraspecial normal subgroups of p-groups --
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§ 159 2-groups all of whose cyclic subgroups A, B with A ∩ B ≠ {1} generate an abelian subgroup --
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§ 160 p-groups, p 〉 2, all of whose cyclic subgroups A, B with A ∩ B ≠ {1} generate an abelian subgroup --
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§ 161 p-groups where all subgroups not contained in the Frattini subgroup are quasinormal --
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§ 162 The centralizer equality subgroup in a p-group --
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§ 163 Macdonald's theorem on p-groups all of whose proper subgroups are of class at most 2 --
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§ 164 Partitions and Hp-subgroups of a p-group --
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§ 165 p-groups G all of whose subgroups containing Φ(G) as a subgroup of index p are minimal nonabelian --
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§ 166 A characterization of p-groups of class 〉 2 all of whose proper subgroups are of class ≤ 2 --
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§ 167 Nonabelian p-groups all of whose nonabelian subgroups contain the Frattini subgroup --
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§ 168 p-groups with given intersections of certain subgroups --
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§ 169 Nonabelian p-groups G with 〈A, B〉 minimal nonabelian for any two distinct maximal cyclic subgroups A, B of G --
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§ 170 p-groups with many minimal nonabelian subgroups, 2 --
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§ 171 Characterizations of Dedekindian 2-groups --
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§ 172 On 2-groups with small centralizers of elements --
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§ 173 Nonabelian p-groups with exactly one noncyclic maximal abelian subgroup --
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§ 174 Classification of p-groups all of whose nonnormal subgroups are cyclic or abelian of type (p, p) --
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§ 175 Classification of p-groups all of whose nonnormal subgroups are cyclic, abelian of type (p, p) or ordinary quaternion --
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§ 176 Classification of p-groups with a cyclic intersection of any two distinct conjugate subgroups --
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§ 177 On the norm of a p-group --
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§ 178 p-groups whose character tables are strongly equivalent to character tables of metacyclic p-groups, and some related topics --
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§ 179 p-groups with the same numbers of subgroups of small indices and orders as in a metacyclic p-group --
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§ 180 p-groups all of whose noncyclic abelian subgroups are normal --
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§ 181 p-groups all of whose nonnormal abelian subgroups lie in the center of their normalizers --
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§ 182 p-groups with a special maximal cyclic subgroup --
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§ 183 p-groups generated by any two distinct maximal abelian subgroups --
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§ 184 p-groups in which the intersection of any two distinct conjugate subgroups is cyclic or generalized quaternion --
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§ 185 2-groups in which the intersection of any two distinct conjugate subgroups is either cyclic or of maximal class --
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§ 186 p-groups in which the intersection of any two distinct conjugate subgroups is either cyclic or abelian of type (p, p) --
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§ 187 p-groups in which the intersection of any two distinct conjugate cyclic subgroups is trivial --
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§ 188 p-groups with small subgroups generated by two conjugate elements --
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§ 189 2-groups with index of every cyclic subgroup in its normal closure ≤ 4 --
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Appendix 45 Varia II --
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Appendix 46 On Zsigmondy primes --
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Appendix 47 The holomorph of a cyclic 2-group --
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Appendix 48 Some results of R. van der Waall and close to them --
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Appendix 49 Kegel's theorem on nilpotence of Hp-groups --
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Appendix 50 Sufficient conditions for 2-nilpotence --
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Appendix 51 Varia III --
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Appendix 52 Normal complements for nilpotent Hall subgroups --
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Appendix 53 p-groups with large abelian subgroups and some related results --
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Appendix 54 On Passman's Theorem 1.25 for p 〉 2 --
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Appendix 55 On p-groups with the cyclic derived subgroup of index p2 --
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Appendix 56 On finite groups all of whose p-subgroups of small orders are normal --
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Appendix 57 p-groups with a 2-uniserial subgroup of order p and an abelian subgroup of type (p, p) --
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Research problems and themes IV --
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Bibliography --
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Author index --
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Subject index --
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Backmatter
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Issued also in print.
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English
Additional Edition:
ISBN 3-11-028148-1
Additional Edition:
ISBN 3-11-028145-7
Language:
English
DOI:
10.1515/9783110281477
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