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Humphreys J.E. — A Course in Group Theory
Humphreys J.E. — A Course in Group Theory



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Название: A Course in Group Theory

Автор: Humphreys J.E.

Аннотация:

This book is a clear and self-contained introduction to the theory of groups. It is written with the aim of stimulating and encouraging undergraduates and first year postgraduates to find out more about the subject. All topics likely to be encountered in undergraduate courses are covered. Numerous worked examples and exercises are included. The exercises have nearly all been tried and tested on students, and complete solutions are given. Each chapter ends with a summary of the material covered and notes on the history and development of group theory. The themes of the book are various classification problems in (finite) group theory. Introductory chapters explain the concepts of group, subgroup and normal subgroup, and quotient group. The Homomorphism and Isomorphism Theorems are then discussed, and, after an introduction to G-sets, the Sylow Theorems are proved. Subsequent chapters deal with finite abelian groups, the Jordan-Holder Theorem, soluble groups, p-groups, and group extensions. Finally there is a discussion of the finite simple groups and their classification, which was completed in the 1980s after a hundred years of effort.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 304

Добавлена в каталог: 01.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$M_{10}$      214
$M_{11}$      213 216
$M_{12}$      217
$M_{22}$, $M_{23}$, $M_{24}$      218
$M_{9}$      214
Additive notation      6
Associativity axiom      1
Aut(G)      70
Automorphism      70
Automorphism, inner      73
Basis      236
Central extension      177 183
Central product      117
Centraliser      90 95
Centre      67 75 155
Chief factors      137
Classification of groups      vii
Classification of groups with $p2q$ elements      109
Classification of groups with $p^2$ elements      95 195 238
Classification of groups with $p^3$ elements      195
Classification of groups with 12 elements      108 196 238 239
Classification of groups with 16 elements      239
Classification of groups with 18 elements      200 239 240
Classification of groups with 20 elements      201 240
Classification of groups with 21 elements      107 240
Classification of groups with 24 elements      110 241
Classification of groups with 27 elements      241
Classification of groups with 28 elements      201 242
Classification of groups with 2p elements      106 238
Classification of groups with 3 elements      26
Classification of groups with 30 elements      109 116 159 242
Classification of groups with 4 elements      26
Classification of groups with 6 elements      45
Classification of groups with 70 elements      201
Classification of groups with 8 elements      46 238
Classification of groups with p elements      44 195 238
Classification of groups with pq elements      195
Classification of groups, finite abelian      120
Closure axiom      1
Code      49 50
Code, error-correcting      49
Code, error-detecting      49
Code, Golay ternary      53 220
Code, ISBN      49
Code, minimum distance      51
Codeword      50
Codeword, weight      51
Commutator      148
Complex Lie algebra      230
Composition factors      137
conjugate      59
Conjugate, element      59
Conjugate, subgroup      59
Coset      38
Coset decoding table      54
Cyclic extension      177 186
Decoding      54
Dynkin diagram      230
Equivalence class      14 39
Extension      174
Field      125
FORM      223—228
Form, alternating      226
Form, bilinear      226
Form, Hermitian      224
Form, kernel      228
Form, matrix of      224
Form, non-degenerate      224
Form, non-singular      228
Form, quadratic      228
Form, sesquilinear      223
Form, symmetric      228
G-set      89
Generating relations      33
Generator matrix      52
Generators      33
Greatest common divisor      235
Group      1
Group, $GL(n, R)$      3
Group, abelian      1
Group, abelian, elementary      126
Group, adjoint Chevalley      230
Group, alternating      83 222
Group, alternating A(n)      144
Group, alternating A(S)      140
Group, automorphism group of cyclic group of order p      192
Group, automorphism group of cyclic Group, automorphism group of group of order $2^n$      193
Group, automorphism group of dihedral group d(3)      195
Group, automorphism group of elementary abelian p-group      193
Group, classical      223
Group, cyclic      2 34—36 44 238
Group, dihedral      4 34 195 198 238
Group, direct product      5 112
Group, direct product, external      113
Group, direct product, internal      113
Group, finite      1
Group, finite abelian      120—127
Group, finite abelian p-      122
Group, finite abelian, type      124
Group, finite simple      202 222
Group, general linear      203
Group, generalised quaternion      196 198 238
Group, hyperoctahedral $B_n$      170
Group, infinite      1
Group, Janko      231
Group, k-transive permutation      218
Group, Mathieu      231
Group, monster      231
Group, nilpotent      156
Group, of Lie type      222 230
Group, orthogonal      228
Group, p-      100
Group, projective special linear      204 223
Group, S(n)      77
Group, S(X)      12
Group, simple      137
Group, soluble      146
Group, special linear      203
Group, sporadic      222 231
Group, sporadic simple      213
Group, Suzuki      231
Group, symplectic      226
Group, table      3
Group, twisted      230
Group, unitary      223
Homomorphism      68
Homomorphism, image      70
Homomorphism, kernel      70
Identity axiom      1
Inverse      10
Inverse axiom      1
Inverse, unique      18
Isomorphism      69
Linear independent      236
MAP      8
Map, bijective      8 11
Map, composite      9
Map, graph      13
Map, identity      10
Map, injective      8
Map, inverse      10 11
Map, isomorphism      13
Map, one-to-one      8
Map, onto      8
Map, surjective      8
Matrix      3 202
Matrix, unitary      224
Multiplicative notation      5
Normaliser      91 96
Orbit      91
Order of a group      41
Order of an element      24 42
orthogonal matrices      229
Parity check matrix      55
Partition      14
Permutable      43
Permutation      12 77
Permutation, cycle notation      77
Permutation, cycle type      84
Permutation, disjoint      78
Permutation, even      82
Permutation, k-cycle      78
Permutation, odd      82
Permutation, transposition      81
Powers      22
Presentation      33
Prime      44
Pullback      118
Quotient group      62
Relation      13 91
Relation, equivalence      14
Relation, reflexive      14
Relation, symmetric      14
Relation, transitive      14
Scalar matrices      204
Section      174
Sectional factor set      175
Semidirect product      163
Series      128—33
Series, chief      133
Series, composition      133
Series, derived      150
Series, isomorphic      129
Series, normal      128
Series, subnormal      128
Series, upper central      155
Spanning set      236
Stabiliser      90
Steiner system      220
Subgroup      30 39
Subgroup, characteristic      139
Subgroup, characteristically simple      139
Subgroup, commutator      149
Subgroup, derived      149
Subgroup, generated by X      32
Subgroup, maximal      156
Subgroup, normal      59
Subgroup, Sylow p-      98
Syndrome      55
Syndrome decoding table      56
Theorem, Cayley      86
Theorem, Correspondence      65
Theorem, first isomorphism      72
Theorem, First Sylow      99
Theorem, Fourth Sylow      102
Theorem, Homomorphism      71
Theorem, Jordan — Holder      128 134
Theorem, Lagrange      41
Theorem, Orbit — Stabiliser      92
Theorem, Schreier's Refinement      132
Theorem, Second Isomorphism      73
Theorem, Second Sylow      100
Theorem, Sylow      98
Theorem, Third Sylow      101
Transitive      214
Transvection      208
Well-defined      15 62 71
Witt index      229
Wreath product      167—73
Wreath product, permutation      170
Wreath product, regular      167
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