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Groups of prime power order. Volume 3
- Author / Creator
- Available as
- Online
- Summary
-
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, cl...
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.
Details
- Creator
- Yakov Berkovich, Zvonimir Janko
- Format
- Books
- Language
- English
- Contributors
- Publication
-
- 1st ed
- Berlin : De Gruyter, 2011
- Physical Details
-
- 1 online resource (668 p.)
- ISBNs
- 1283400375, 9786613400376, 3110254484, 3110207176
- OCLC
- ocn743693632, ocn900775515, ocn978483275
- Includes indexes.
- Issued also in print.
- English
- Frontmatter -- Contents -- List of definitions and notations -- Preface -- Prerequisites from Volumes 1 and 2 -- §93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4 -- §94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4 -- §95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e -- §96 Groups with at most two conjugate classes of nonnormal subgroups -- §97 p-groups in which some subgroups are generated by elements of order p -- §98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n 3 fixed -- §99 2-groups with sectional rank at most 4 -- §100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- §101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- §102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- §103 Some results of Jonah and Konvisser -- §104 Degrees of irreducible characters of p-groups associated with finite algebras -- §105 On some special p-groups -- §106 On maximal subgroups of two-generator 2-groups -- §107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups -- §108 p-groups with few conjugate classes of minimal nonabelian subgroups -- §109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p -- §110 Equilibrated p-groups -- §111 Characterization of abelian and minimal nonabelian groups -- §112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order -- §113 The class of 2-groups in §70 is not bounded -- §114 Further counting theorems -- §115 Finite p-groups all of whose maximal subgroups except one are extraspecial -- §116 Groups covered by few proper subgroups -- §117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class -- §118 Review of characterizations of p-groups with various minimal nonabelian subgroups -- §119 Review of characterizations of p-groups of maximal class -- §120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection -- §121 p-groups of breadth 2 -- §122 p-groups all of whose subgroups have normalizers of index at most p -- §123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes -- §124 The number of subgroups of given order in a metacyclic p-group -- §125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant -- §126 The existence of p-groups G1 G such that Aut(G1) Aut(G) -- §127 On 2-groups containing a maximal elementary abelian subgroup of order 4 -- §128 The commutator subgroup of p-groups with the subgroup breadth 1 -- §129 On two-generator 2-groups with exactly one maximal subgroup which is not two-generator -- §130 Soft subgroups of p-groups -- §131 p-groups with a 2-uniserial subgroup of order p -- §132 On centralizers of elements in p-groups -- §133 Class and breadth of a p-group -- §134 On p-groups with maximal elementary abelian subgroup of order p2 -- §135 Finite p-groups generated by certain minimal nonabelian subgroups -- §136 p-groups in which certain proper nonabelian subgroups are two-generator -- §137 p-groups all of whose proper subgroups have its derived subgroup of order at most p -- §138 p-groups all of whose nonnormal subgroups have the smallest possible normalizer -- §139 p-groups with a noncyclic commutator group all of whose proper subgroups have a cyclic commutator group -- §140 Power automorphisms and the norm of a p-group -- §141 Nonabelian p-groups having exactly one maximal subgroup with a noncyclic center -- §142 Nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal nonabelian -- §143 Alternate proof of the Reinhold Baer theorem on 2-groups with nonabelian norm -- §144 p-groups with small normal closures of all cyclic subgroups -- Appendix 27 Wreathed 2-groups -- Appendix 28 Nilpotent subgroups -- Appendix 29 Intersections of subgroups -- Appendix 30 Thompson's lemmas -- Appendix 31 Nilpotent p'-subgroups of class 2 in GL(n, p) -- Appendix 32 On abelian subgroups of given exponent and small index -- Appendix 33 On Hadamard 2-groups -- Appendix 34 Isaacs-Passman's theorem on character degrees -- Appendix 35 Groups of Frattini class 2 -- Appendix 36 Hurwitz' theorem on the composition of quadratic forms -- Appendix 37 On generalized Dedekindian groups -- Appendix 38 Some results of Blackburn and Macdonald -- Appendix 39 Some consequences of Frobenius' normal p-complement theorem -- Appendix 40 Varia -- Appendix 41 Nonabelian 2-groups all of whose minimal nonabelian subgroups have cyclic centralizers -- Appendix 42 On lattice isomorphisms of p-groups of maximal class -- Appendix 43 Alternate proofs of two classical theorems on solvable groups and some related results -- Appendix 44 Some of Freiman's results on finite subsets of groups with small doubling -- Research problems and themes III -- Author index -- Subject index