Groups of prime power order. Volume 5 / Yakov Berkovich and Zvonimir Janko ; edited by Victor P. Maslov [and five others].

Format:

Book

Author/Creator:

Berkovich, I︠A︡. G., 1938- author.

Janko, Zvonimir, 1932- author.

Contributor:

Maslov, V. P. (Viktor Pavlovich), editor.

Series:

De Gruyter expositions in mathematics ; Volume 62.

De Gruyter Expositions in Mathematics, 0938-6572 ; Volume 62

Language:

English

Subjects (All):

Finite groups.

Group theory.

Physical Description:

1 online resource (434 p.)

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2016.

Language Note:

English

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.

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

§ 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

§ 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

Notes:

Description based upon print version of record.

Includes bibliographical references and indexes.

Description based on online resource; title from PDF title page (ebrary, viewed February 10, 2016).

ISBN:

9783110295351

3110295350

9783110389043

3110389045

OCLC:

951149639