Groups of Prime Power Order. / Volume 5 / / Yakov G. Berkovich, Zvonimir Janko.
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...
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Superior document: | Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2016] ©2016 |
Year of Publication: | 2016 |
Language: | English |
Series: | De Gruyter Expositions in Mathematics ,
62 |
Online Access: | |
Physical Description: | 1 online resource (413 p.) |
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Other title: | 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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Summary: | 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 research problems and themes. |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110295351 9783110494969 9783110762501 9783110701005 9783110485103 9783110485288 |
ISSN: | 0938-6572 ; |
DOI: | 10.1515/9783110295351 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Yakov G. Berkovich, Zvonimir Janko. |