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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Berkovich, Yakov
Otros Autores: Janko, Zvonimir
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin : De Gruyter, 2011.
Temas:
Finite groups.
Group theory.
Groupes finis.
Théorie des groupes.
Finite groups
Group theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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

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