UID:
almahu_9949462113802882
Format:
1 online resource (639 p.)
ISBN:
9783110254488
,
9783110494969
Series Statement:
De Gruyter Expositions in Mathematics , 56
Content:
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.
Note:
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 --
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§ 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 --
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§ 144 p-groups with small normal closures of all cyclic subgroups --
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A.27 Wreathed 2-groups --
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A.28 Nilpotent subgroups --
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A.29 Intersections of subgroups --
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A.30 Thompson's lemmas --
,
A.31 Nilpotent p'-subgroups of class 2 in GL(n, p) --
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A.32 On abelian subgroups of given exponent and small index --
,
A.33 On Hadamard 2-groups --
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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 --
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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
,
Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Expositions in Mathematics Backlist eBook Package, De Gruyter, 9783110494969
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202
Additional Edition:
ISBN 9783110207170
Language:
English
DOI:
10.1515/9783110254488
URL:
https://doi.org/10.1515/9783110254488
URL:
https://www.degruyter.com/isbn/9783110254488
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