000			11053nam a22004933i 4500
001			EBC5516054
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005			20240724113337.0
006			m o d |
007			cr cnu||||||||
008			240724s2018 xx o ||||0 eng d
020			_a9783110533149 _q(electronic bk.)
020			_z9783110530971
035			_a(MiAaPQ)EBC5516054
035			_a(Au-PeEL)EBL5516054
035			_a(OCoLC)1054067465
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA171 .B475 2018
100	1		_aBerkovich, Yakov G.
245	1	0	_aGroups of Prime Power Order. Volume 6.
250			_a1st ed.
264		1	_aBerlin/Boston : _bWalter de Gruyter GmbH, _c2018.
264		4	_c©2018.
300			_a1 online resource (410 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aDe Gruyter Expositions in Mathematics Series ; _vv.65
505	0		_aIntro -- Contents -- List of definitions and notations -- Preface -- 257 Nonabelian p-groups with exactly one minimal nonabelian subgroup of exponent &amp -- gt -- p -- 258 2-groups with some prescribed minimal nonabelian subgroups -- 259 Nonabelian p-groups, p &amp -- gt -- 2, all of whose minimal nonabelian subgroups are isomorphic to M&lt -- sub&gt -- p&lt -- /sub&gt -- &lt -- sup&gt -- 3&lt -- /sup&gt -- -- 260 p-groups with many modular subgroups M&lt -- sub&gt -- p&lt -- /sub&gt -- &lt -- sup&gt -- n&lt -- /sup&gt -- -- 261 Nonabelian p-groups of exponent &amp -- gt -- p with a small number of maximal abelian subgroups of exponent &amp -- gt -- p -- 262 Nonabelian p-groups all of whose subgroups are powerful -- 263 Nonabelian 2-groups G with C&lt -- sub&gt -- G&lt -- /sub&gt -- (x) ≤ H for all H ∈ Γ&lt -- sub&gt -- 1&lt -- /sub&gt -- and x ∈ H − Z(G) -- 264 Nonabelian 2-groups of exponent ≥ 16 all of whose minimal nonabelian subgroups, except one, have order 8 -- 265 p-groups all of whose regular subgroups are either absolutely regular or of exponent p -- 266 Nonabelian p-groups in which any two distinct minimal nonabelian subgroups with a nontrivial intersection are non-isomorphic -- 267 Thompson's A × B lemma -- 268 On automorphisms of some p-groups -- 269 On critical subgroups of p-groups -- 270 p-groups all of whose A&lt -- sub&gt -- k&lt -- /sub&gt -- -subgroups for a fixed k &amp -- gt -- 1 are metacyclic -- 271 Two theorems of Blackburn -- 272 Nonabelian p-groups all of whose maximal abelian subgroups, except one, are either cyclic or elementary abelian -- 273 Nonabelian p-groups all of whose noncyclic maximal abelian subgroups are elementary abelian -- 274 Non-Dedekindian p-groups in which any two nonnormal subgroups normalize each other.
505	8		_a275 Nonabelian p-groups with exactly p normal closures of minimal nonabelian subgroups -- 276 2-groups all of whose maximal subgroups, except one, are Dedekindian -- 277 p-groups with exactly two conjugate classes of nonnormal maximal cyclic subgroups -- 278 Nonmetacyclic p-groups all of whose maximal metacyclic subgroups have index p -- 279 Subgroup characterization of some p-groups of maximal class and close to them -- 280 Nonabelian p-groups all of whose maximal subgroups, except one, are minimal nonmetacyclic -- 281 Nonabelian p-groups in which any two distinct minimal nonabelian subgroups have a cyclic intersection -- 282 p-groups with large normal closures of nonnormal subgroups -- 283 Nonabelian p-groups with many cyclic centralizers -- 284 Nonabelian p-groups, p &amp -- gt -- 2, of exponent &amp -- gt -- p&lt -- sup&gt -- 2&lt -- /sup&gt -- all of whose minimal nonabelian subgroups are of order p&lt -- sup&gt -- 3&lt -- /sup&gt -- -- 285 A generalization of Lemma 57.1 -- 286 Groups ofexponent p with many normal subgroups -- 287 p-groups in which the intersection of any two nonincident subgroups is normal -- 288 Nonabelian p-groups in which for every minimal nonabelian M &amp -- lt -- G and x ∈ G − M, we have C&lt -- sub&gt -- M&lt -- /sub&gt -- (x) = Z(M) -- 289 Non-Dedekindian p-groups all of whose maximal nonnormal subgroups are conjugate -- 290 Non-Dedekindian p-groups G with a noncyclic proper subgroup H such that each subgroup which is nonincident with H is normal in G -- 291 Nonabelian p-groups which are generated by a fixed maximal cyclic subgroup and any minimal nonabelian subgroup -- 292 Nonabelian p-groups generated by any two non-conjugate minimal nonabelian subgroups -- 293 Exercises -- 294 p-groups, p &amp -- gt -- 2, whose Frattini subgroup is nonabelian metacyclic.
505	8		_a295 Any irregular p-group contains a non-isolated maximal regular subgroup -- 296 Non-Dedekindian p-groups all of whose nonnormal maximal cyclic subgroups are C-equivalent -- 298 Non-Dedekindian p-groups all of whose subgroups of order ≤ p&lt -- sup&gt -- s&lt -- /sup&gt -- (s ≥ 1 fixed) are normal -- 299 On p'-automorphisms of p-groups -- 300 On p-groups all of whose maximal subgroups of exponent p are normal and have order p&lt -- sup&gt -- p&lt -- /sup&gt -- -- 301 p-groups of exponent &amp -- gt -- p containing &amp -- lt -- p maximal abelian subgroups of exponent &amp -- gt -- p -- 302 Alternate proof of Theorem 109.1 -- 303 Nonabelian p-groups of order &amp -- gt -- p&lt -- sup&gt -- 4&lt -- /sup&gt -- all of whose subgroups of order p&lt -- sup&gt -- 4&lt -- /sup&gt -- are isomorphic -- 304 Non-Dedekindian p-groups in which each nonnormal subgroup has a cyclic complement in its normalizer -- 305 Nonabelian p-groups G all of whose minimal nonabelian subgroups M satisfy Z(M) ≤ Z(G) -- 306 Nonabelian 2-groups all of whose maximal subgroups, except one, are quasi-Hamiltonian or abelian -- 307 Nonabelian p-groups, p &amp -- gt -- 2, all of whose maximal subgroups, except one, are quasi-Hamiltonian or abelian -- 308 Nonabelian p-groups with an elementary abelian intersection of any two distinct maximal abelian subgroups -- 309 Minimal non-p-central p-groups -- 310 Nonabelian p-groups in which each element in any minimal nonabelian subgroup is half-central -- 311 Nonabelian p-groups G of exponent p in which C&lt -- sub&gt -- G&lt -- /sub&gt -- (x) = &amp -- lt -- x&amp -- gt -- G for all noncentral x ∈ G -- 312 Nonabelian 2-groups all of whose minimal nonabelian subgroups, except one, are isomorphic to M&lt -- sub&gt -- 2&lt -- /sub&gt -- (2, 2) = &amp -- lt -- a, b / a&lt -- sup&gt -- 4&lt -- /sup&gt -- = b&lt.
505	8		_asup&gt -- 4&lt -- /sup&gt -- = 1, a&lt -- sup&gt -- b&lt -- /sup&gt -- = a&lt -- sup&gt -- −1&lt -- /sup&gt -- &amp -- gt -- -- 313 Non-Dedekindian 2-groups all of whose maximal Dedekindian subgroups have index 2 -- 314 Theorem of Glauberman-Mazza on p-groups with a nonnormal maximal elementary abelian subgroup of order p&lt -- sup&gt -- 2&lt -- /sup&gt -- -- 315 p-groups with some non-p-central maximal subgroups -- 316 Nonabelian p-groups, p &amp -- gt -- 2, of exponent &amp -- gt -- p&lt -- sup&gt -- 3&lt -- /sup&gt -- all of whose minimal nonabelian subgroups, except one, have order p&lt -- sup&gt -- 3&lt -- /sup&gt -- -- 317 Nonabelian p-groups, p &amp -- gt -- 2, all of whose minimal nonabelian subgroups are isomorphic to M&lt -- sub&gt -- p&lt -- /sub&gt -- (2, 2) -- 318 Nonabelian p-groups, p &amp -- gt -- 2, of exponent &amp -- gt -- p&lt -- sup&gt -- 2&lt -- /sup&gt -- all of whose minimal nonabelian subgroups, except one, are isomorphic to M&lt -- sub&gt -- p&lt -- /sub&gt -- (2, 2) -- 319 A new characterization of p-central p-groups -- 320 Nonabelian p-groups with exactly one non-p-central minimal nonabelian subgroup -- 321 Nonabelian p-groups G in which each element in G − Φ(G) is half-central -- 322 Nonabelian p-groups G such that C&lt -- sub&gt -- G&lt -- /sub&gt -- (H) = Z(G) for any nonabelian H ≤ G -- 323 Nonabelian p-groups that are not generated by its noncyclic abelian subgroups -- 324 A separation of metacyclic and nonmetacyclic minimal nonabelian subgroups in nonabelian p-groups -- 325 p-groups which are not generated by their nonnormal subgroups, 2 -- 326 Nonabelian p-groups all of whose maximal abelian subgroups are normal -- Appendix 110 Non-absolutely regular p-groups all of whose maximal absolutely regular subgroups have index p -- Appendix 111 Nonabelian p-groups of exponent &amp -- gt.
505	8		_ap all of whose maximal abelian subgroups of exponent &amp -- gt -- p are isolated -- Appendix 112 Metacyclic p-groups with an abelian maximal subgroup -- Appendix 113 Nonabelian p-groups with a cyclic intersection of any two distinct maximal abelian subgroups -- Appendix 114 An analog of Thompson's dihedral lemma -- Appendix 115 Some results from Thompson' papers and the Odd Order paper -- Appendix 116 On normal subgroups of a p-group -- Appendix 117 Theorem of Mann -- Appendix 118 On p-groups with given isolated subgroups -- Appendix 119 Two-generator normal subgroups of a p-group G that contained in Φ(G) are metacyclic -- Appendix 120 Alternate proofs of some counting theorems -- Appendix 121 On p-groups of maximal class -- Appendix 122 Criteria of regularity -- Appendix 123 Nonabelian p-groups in which any two nonincident subgroups have an abelian intersection -- Appendix 124 Characterizations of the p-groups of maximal class and the primary ECF-groups -- Appendix 125 Nonabelian p-groups all of whose proper nonabelian subgroups have exponent p -- Appendix 126 On p-groups with abelian automorphism groups -- Appendix 127 Alternate proof of Proposition 1.23 -- Appendix 128 Alternate proof of the theorem of Passman on p-groups all of whose subgroups of order ≤ p&lt -- sup&gt -- s&lt -- /sup&gt -- (s ≥ 1 is fixed) are normal -- Appendix 129 Alternate proofs of Theorems 309.1 and 309.2 on minimal non-p-central p-groups -- Appendix 130 Non-Dedekindian p-groups all of whose nonnormal maximal cyclic subgroups are conjugate -- Appendix 131 A characterization of some 3-groups of maximal class -- Appendix 132 Alternate approach to classification of minimal non-p-central p-groups -- Appendix 133 Nonabelian p-groups all of whose minimal nonabelian subgroups are isomorphic to Mp(n, n) or M&lt -- sub&gt -- p&lt -- /sub&gt -- (n, n, 1) for a fixed natural n &amp.
505	8		_agt.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aFinite groups.
655		4	_aElectronic books.
700	1		_aJanko, Zvonimir.
776	0	8	_iPrint version: _aBerkovich, Yakov G. _tGroups of Prime Power Order. Volume 6 _dBerlin/Boston : Walter de Gruyter GmbH,c2018 _z9783110530971
797	2		_aProQuest (Firm)
830		3	_aDe Gruyter Expositions in Mathematics Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5516054 _zClick to View
999			_c5106 _d5106