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Berkovich, Yakov; Janko, Zvonimir.
This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: impact of minimal nonabelian subgroups on the structure of p-groups, classification of groups all of whose nonnormal subgroups have the same order, degrees of irreducible cha...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Berkovich, Yakov. | |
| 245 | 1 | 0 | |a Berkovich, Yakov; Janko, Zvonimir. |
| 260 | |a Berlin : |b De Gruyter, |c 2011. | ||
| 300 | |a 1 online resource (668 pages) | ||
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| 337 | |a computer |b c |2 rdamedia | ||
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t List of definitions and notations -- |t Preface -- |t Prerequisites from Volumes 1 and 2 -- |t §93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4 -- |t §94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4 -- |t §95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e -- |t §96 Groups with at most two conjugate classes of nonnormal subgroups -- |t §97 p-groups in which some subgroups are generated by elements of order p -- |t §98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n 3 fixed -- |t §99 2-groups with sectional rank at most 4 -- |t §100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- |t §101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- |t §102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- |t §103 Some results of Jonah and Konvisser -- |t §104 Degrees of irreducible characters of p-groups associated with finite algebras -- |t §105 On some special p-groups -- |t §106 On maximal subgroups of two-generator 2-groups -- |t §107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups -- |t §108 p-groups with few conjugate classes of minimal nonabelian subgroups -- |t §109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p -- |t §110 Equilibrated p-groups -- |t §111 Characterization of abelian and minimal nonabelian groups -- |t §112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order -- |t §113 The class of 2-groups in §70 is not bounded -- |t §114 Further counting theorems -- |t §115 Finite p-groups all of whose maximal subgroups except one are extraspecial -- |t §116 Groups covered by few proper subgroups -- |t §117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class -- |t §118 Review of characterizations of p-groups with various minimal nonabelian subgroups -- |t §119 Review of characterizations of p-groups of maximal class -- |t §120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection -- |t §121 p-groups of breadth 2 -- |t §122 p-groups all of whose subgroups have normalizers of index at most p -- |t §123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes -- |t §124 The number of subgroups of given order in a metacyclic p-group -- |t §125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant -- |t §126 The existence of p-groups G1 G such that Aut(G1) Aut(G) -- |t §127 On 2-groups containing a maximal elementary abelian subgroup of order 4 -- |t §128 The commutator subgroup of p-groups with the subgroup breadth 1 -- |t §129 On two-generator 2-groups with exactly one maximal subgroup which is not two-generator -- |t §130 Soft subgroups of p-groups -- |t §131 p-groups with a 2-uniserial subgroup of order p -- |t §132 On centralizers of elements in p-groups -- |t §133 Class and breadth of a p-group -- |t §134 On p-groups with maximal elementary abelian subgroup of order p2 -- |t §135 Finite p-groups generated by certain minimal nonabelian subgroups -- |t §136 p-groups in which certain proper nonabelian subgroups are two-generator -- |t §137 p-groups all of whose proper subgroups have its derived subgroup of order at most p -- |t §138 p-groups all of whose nonnormal subgroups have the smallest possible normalizer -- |t §139 p-groups with a noncyclic commutator group all of whose proper subgroups have a cyclic commutator group -- |t §140 Power automorphisms and the norm of a p-group -- |t §141 Nonabelian p-groups having exactly one maximal subgroup with a noncyclic center -- |t §142 Nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal nonabelian -- |t §143 Alternate proof of the Reinhold Baer theorem on 2-groups with nonabelian norm -- |t §144 p-groups with small normal closures of all cyclic subgroups -- |t Appendix 27 Wreathed 2-groups -- |t Appendix 28 Nilpotent subgroups -- |t Appendix 29 Intersections of subgroups -- |t Appendix 30 Thompson's lemmas -- |t Appendix 31 Nilpotent p'-subgroups of class 2 in GL(n, p) -- |t Appendix 32 On abelian subgroups of given exponent and small index -- |t Appendix 33 On Hadamard 2-groups -- |t Appendix 34 Isaacs-Passman's theorem on character degrees -- |t Appendix 35 Groups of Frattini class 2 -- |t Appendix 36 Hurwitz' theorem on the composition of quadratic forms -- |t Appendix 37 On generalized Dedekindian groups -- |t Appendix 38 Some results of Blackburn and Macdonald -- |t Appendix 39 Some consequences of Frobenius' normal p-complement theorem -- |t Appendix 40 Varia -- |t Appendix 41 Nonabelian 2-groups all of whose minimal nonabelian subgroups have cyclic centralizers -- |t Appendix 42 On lattice isomorphisms of p-groups of maximal class -- |t Appendix 43 Alternate proofs of two classical theorems on solvable groups and some related results -- |t Appendix 44 Some of Freiman's results on finite subsets of groups with small doubling -- |t Research problems and themes III -- |t Author index -- |t Subject index |
| 520 | |a This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: impact of minimal nonabelian subgroups on the structure of p-groups, classification of groups all of whose nonnormal subgroups have the same order, degrees of irreducible characters of p-groups associated with finite algebras, groups covered by few proper subgroups, p-groups of element breadth 2 and subgroup breadth 1, exact number of subgroups of given order in a metacyclic p-group, soft subgroups, p-groups with a maximal elementary abelian subgroup of order p2, p-groups generated by certain minimal nonabelian subgroups, p-groups in which certain nonabelian subgroups are 2-generator. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Finite groups. | |
| 650 | 0 | |a Group theory. | |
| 650 | 6 | |a Groupes finis. | |
| 650 | 6 | |a Théorie des groupes. | |
| 650 | 7 | |a Finite groups |2 fast | |
| 650 | 7 | |a Group theory |2 fast | |
| 700 | 1 | |a Janko, Zvonimir. | |
| 776 | 0 | 8 | |i Print version: |a Berkovich, Yakov. |t Berkovich, Yakov; Janko, Zvonimir: Groups of Prime Power Order. Volume 3. |d Berlin : De Gruyter, ©2011 |z 9783112189092 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=737006 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL737006 | ||
| 938 | |a YBP Library Services |b YANK |n 6928023 | ||
| 994 | |a 92 |b IZTAP | ||