Groups of prime power order [online] / Yakov G. Berkovich, Zvonimir Janko

vol. 4 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 § 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

vol. 5 Frontmatter Contents List of definitions and notations Preface § 190. On p-groups containing a subgroup of maximal class and index p § 191. p-groups G all of whose nonnormal subgroups contain G′ in its normal closure § 192. p-groups with all subgroups isomorphic to quotient groups § 193. Classification of p-groups all of whose proper subgroups are s-self-dual § 194. p-groups all of whose maximal subgroups, except one, are s-self-dual § 195. Nonabelian p-groups all of whose subgroups are q-self-dual § 196. A p-group with absolutely regular normalizer of some subgroup § 197. Minimal non-q-self-dual 2-groups § 198. Nonmetacyclic p-groups with metacyclic centralizer of an element of order p § 199. p-groups with minimal nonabelian closures of all nonnormal abelian subgroups § 200. The nonexistence of p-groups G all of whose minimal nonabelian subgroups intersect Z(G) trivially § 201. Subgroups of order pp and exponent p in p-groups with an irregular subgroup of maximal class and index > p § 202. p-groups all of whose A2-subgroups are metacyclic § 203. Nonabelian p-groups G in which the center of each nonabelian subgroup is contained in Z(G) § 204. Theorem of R. van der Waal on p-groups with cyclic derived subgroup, p > 2 § 205. Maximal subgroups of A2-groups § 206. p-groups all of whose minimal nonabelian subgroups are pairwise nonisomorphic § 207. Metacyclic groups of exponent pe with a normal cyclic subgroup of order pe § 208. Non-Dedekindian p-groups all of whose nonnormal maximal cyclic subgroups are maximal abelian § 209. p-groups with many minimal nonabelian subgroups, 3 § 210. A generalization of Dedekindian groups
§ 211. Nonabelian p-groups generated by the centers of their maximal subgroups § 212. Nonabelian p-groups generated by any two nonconjugate maximal abelian subgroups § 213. p-groups with A ∩ B being maximal in A or B for any two nonincident subgroups A and B § 214. Nonabelian p-groups with a small number of normal subgroups § 215. Every p-group of maximal class and order ≥ pp, p > 3, has exactly p two-generator nonabelian subgroups of index p § 216. On the theorem of Mann about p-groups all of whose nonnormal subgroups are elementary abelian § 217. Nonabelian p-groups all of whose elements contained in any minimal nonabelian subgroup are of breadth < 2 § 218. A nonabelian two-generator p-group in which any nonabelian epimorphic image has the cyclic center § 219. On “large” elementary abelian subgroups in p-groups of maximal class § 220. On metacyclic p-groups and close to them § 221. Non-Dedekindian p-groups in which normal closures of nonnormal abelian subgroups have cyclic centers § 222. Characterization of Dedekindian p-groups, 2 § 223. Non-Dedekindian p-groups in which the normal closure of any nonnormal cyclic subgroup is nonabelian § 224. p-groups in which the normal closure of any cyclic subgroup is abelian § 225. Nonabelian p-groups in which any s (a fixed s ∈ {3, . . . , p + 1}) pairwise noncommuting elements generate a group of maximal class § 226. Noncyclic p-groups containing only one proper normal subgroup of a given order § 227. p-groups all of whose minimal nonabelian subgroups have cyclic centralizers § 228. Properties of metahamiltonian p-groups § 229. p-groups all of whose cyclic subgroups of order ≥ p3 are normal § 230. Nonabelian p-groups of exponent pe all of whose cyclic subgroups of order pe are normal § 231. p-groups which are not generated by their nonnormal subgroups § 232. Nonabelian p-groups in which any nonabelian subgroup contains its centralizer § 233. On monotone p-groups § 234. p-groups all of whose maximal nonnormal abelian subgroups are conjugate § 235. On normal subgroups of capable 2-groups § 236. Non-Dedekindian p-groups in which the normal closure of any cyclic subgroup has a cyclic center § 237. Noncyclic p-groups all of whose nonnormal maximal cyclic subgroups are self-centralizing § 238. Nonabelian p-groups all of whose nonabelian subgroups have a cyclic center § 239. p-groups G all of whose cyclic subgroups are either contained in Z(G) or avoid Z(G) § 240. p-groups G all of whose nonnormal maximal cyclic subgroups are conjugate § 241. Non-Dedekindian p-groups with a normal intersection of any two nonincident subgroups § 242. Non-Dedekindian p-groups in which the normal closures of all nonnormal subgroups coincide § 243. Nonabelian p-groups G with Φ(H) = H′ for all nonabelian H ≤ G § 244. p-groups in which any two distinct maximal nonnormal subgroups intersect in a subgroup of order ≤ p § 245. On 2-groups saturated by nonabelian Dedekindian subgroups § 246. Non-Dedekindian p-groups with many normal subgroups § 247. Nonabelian p-groups all of whose metacyclic sections are abelian § 248. Non-Dedekindian p-groups G such that HG = HZ(G) for all nonnormal H < G § 249. Nonabelian p-groups G with A ∩ B = Z(G) for any two distinct maximal abelian subgroups A and B § 250. On the number of minimal nonabelian subgroups in a nonabelian p-group § 251. p-groups all of whose minimal nonabelian subgroups are isolated § 252. Nonabelian p-groups all of whose maximal abelian subgroups are isolated § 253. Maximal abelian subgroups of p-groups, 2 § 254. On p-groups with many isolated maximal abelian subgroups § 255. Maximal abelian subgroups of p-groups, 3 § 256. A problem of D. R. Hughes for 3-groups Appendix 58 – Appendix 109 Research problems and themes V Bibliography Author index Subject index Backmatter

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