دانلود کتاب Groups of Prime Power Order

فهرست مطالب :

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 ∅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 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