Groups of Prime Power Order. / Volume 3 / / Yakov Berkovich, Zvonimir Janko.

• Superior document: Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
• VerfasserIn: Berkovich, Yakov,; Janko, Zvonimir,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2011
• Year of Publication: 2011
• Language: English
• Series: De Gruyter Expositions in Mathematics , 56
• Physical Description: 1 online resource (639 p.)
• Other title: 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 --; A.27 Wreathed 2-groups --; A.28 Nilpotent subgroups --; A.29 Intersections of subgroups --; A.30 Thompson’s lemmas --; A.31 Nilpotent p'-subgroups of class 2 in GL(n, p) --; A.32 On abelian subgroups of given exponent and small index --; A.33 On Hadamard 2-groups --; A.34 Isaacs–Passman’s theorem on character degrees --; A.35 Groups of Frattini class 2 --; A.36 Hurwitz’ theorem on the composition of quadratic forms --; A.37 On generalized Dedekindian groups --; A.38 Some results of Blackburn and Macdonald --; A.39 Some consequences of Frobenius’ normal p-complement theorem --; A.40 Varia --; A.41 Nonabelian 2-groups all of whose minimal nonabelian subgroups have cyclic centralizers --; A.42 On lattice isomorphisms of p-groups of maximal class --; A.43 Alternate proofs of two classical theorems on solvable groups and some related results --; A.44 Some of Freiman’s results on finite subsets of groups with small doubling --; Research problems and themes III --; Author index --; Subject index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110254488; 9783110494969; 9783110238570; 9783110238471; 9783110637205; 9783110261189; 9783110261233; 9783110261202
• ISSN: 0938-6572
• DOI: 10.1515/9783110254488
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Yakov Berkovich, Zvonimir Janko.

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.