Groups of Prime Power Order. / Volume 5 / / 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, , [2016]; ©2016
• Year of Publication: 2016
• Language: English
• Series: De Gruyter Expositions in Mathematics , 62
• Physical Description: 1 online resource (413 p.)

This is the fifth volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume include theory of linear algebras and Lie algebras. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 researc...

Table of Contents

• 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