Alperin J.L., Bell R.B. — Groups and Representations, Vol. 0 :: Электронная библиотека попечительского совета мехмата МГУ

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Alperin J.L., Bell R.B. — Groups and Representations, Vol. 0

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Название: Groups and Representations, Vol. 0

Авторы: Alperin J.L., Bell R.B.

Аннотация:

The aim of this book is to provide a concise treatment of some topics from group theory and representation theory for a one term course. It focuses on the non-commutative side of the field emphasizing the general linear group as the most important group and example. The book will enable graduate students from every mathematical field, as well as strong undergraduates with an interest in algebra, to solidify their knowledge of group theory. The reader should have a familiarity with groups, rings, and fields, along with a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to expose the reader to additional topics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1995

Количество страниц: 212

Добавлена в каталог: 03.03.2008

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Предметный указатель

2-coboundary      84
2-cocycle      84
Abelian group      2
Affine group      102
Algebra      114
Algebraic integer      179
Alternating group      8
Annihilator      131
Augmentation ideal      118
Automorphism      9
Automorphism group      14
Balanced map      111
Bimodule      109
Block      32
BN-pair      48
Borel subgroup      42 48
Brauer, Richard      138
Bruhat decomposition      45 48
Burnside ring      36
Burnside’s Theorem      100 182
Cauchy’s Theorem      66
Cayley’s Theorem      28
Center      14
Central series      103
centralizer      33
CHARACTER      139
Character table      146
Character table of $A_{5}$       159
Character table of $\Sigma_{3}$       156
Character table of $\Sigma_{4}$       157
Character table of GL(2,g)      174
Characteristic subgroup      17
Chief factor      93
Chief series      92
Class function      143
Coboundary      119
Cocycle      119
Cohomology of groups      119
Common annihilator      131
Commutator      2 17
Complement      81
Complete flag      49
Composition factor      89
Composition series      89
Conjugacy class      34
Conjugate elements      7
Conjugate splitting maps      119
Conjugate subgroups      9
Conjugation homomorphism      21
Correspondence theorem      11
Coset      5
Coset representatives      6
Coset space      5
Cycle structure      8
Cyclic group      3
Derived group      17
Derived series      95
Diagonal matrix      41
Dickson L.E.      59 118
Dihedral group      24
Direct product      18
Direct sum      110
Disjoint cycle decomposition      7
Distinct simple modules      122
Double coset      34
Doubly transitive action      31
Dual module      116
Elementary abelian p-group      41
Endomorphism      9
Endomorphism algebra      125
Epimorphism      9
Equivalence of extensions      86
Equivalence of factor pairs      85
Equivalence of representations      118
Equivalence of series      91
Exceptional characters      172
EXPONENT      12 40
Extension      26
Factor pair      26 85
Factorization of indices      6
Faithful action      28
Feit — Thompsion theorem      100
Finite group      2
First isomorphism theorem      11
Fitting subgroup      80
Fixed-point-free map      172
Flag      51
Frattini argument      75
Frattini subgroup      80
Frobenius complement      172
Frobenius group      172
Frobenius kernel      172
Frobenius reciprocity      165
Frobenius, Georg      139 166
Frobenius’ theorem      170
Fundamental theorem on homomorphisms      10
G-set      27
Galois, Evariste      101
General linear group      39
Goursat’s theorem      25
Group      1
Group action      27
Group algebra      114
Group ring      113
Groups of order $p^{3}$       77
Groups of order pq      67
Hall subgroup      81
Hall, Philip      99 101
Higman, Graham      152
Hoelder, Otto      71
Homomorphism of algebras      114
Homomorphism of G-sets      29
Homomorphism of groups      8
Homomorphism of modules      110
Image      10 110
Incident sections      13
Index of a subgroup      5
Induced character      166
Induced module      164
Induction-restriction table      166
Infinite group      2
Inner automorphism      14
Inner product      144
Involution      24
Irreducible character      140

Isomorphism      9
Jacobson, Nathan      131
Jordan — Hoelder theorem      91 110
Jordan, Camille      59
Kernel      10 110
Kernel of a character      149
Klein four-group      8
Kolchin’s theorem      50
Lagrange’s Theorem      3
Levi complement      51
Linear character      140
Linear group action      107
Linear representation      108
Lower central series      105
Maschke’s Theorem      116
Maximal normal subgroup      90
Maximal subgroup      31 73
Minimal normal subgroup      93
Modular representation      118
Module      108
Monomial matrix      48
Monorphism      9
Moore, E.H.      40 59
Natural map      10
Nilpotency class      105
Nilpotent algebra      129
Nilpotent element      129
Nilpotent group      76 103
Nilpotent ideal      129
Normal series      92
Normal subgroup      6
Normalized cochain      118
Normalized section      26
normalizer      34
Opposite algebra      125
Opposite ring      109
Orbit      29
Order of a group      2
Order of an element      2
Ordinary representation      117
Outer automorphism group      14
P-element      63
p-group      63
p-local subgroup      70
Parabolic subgroup      51
Perfect, group      95
Periodic group      2
Permutation      7
Permutation group      28
Permutation matrix      42
Permutation module      115
Primitive action      32
Primitive root      16
Principal character      140
Projective general linear group      58
Projective space      61
Projective special linear group      58
Proper subgroup      3
Quaternion group      26 79
Quotient group      7
Quotient module      110
Radical      131 136
Radical series      136
Refinement of series      92
Regular character      139
Relatively free module      173
Restriction      165
Ring with unit      108
Root subgroup      44
Scalar matrix      58
Schreier refinement theorem      95
Schur — Zassenhaus theorem      81
Schur’s lemma      111
Second cohomology group      84 87
Second isomorphism theorem      12
Section of a group      13 25
Self-normalizing subgroup      37
Semidirect product      20 22
Semisimple module      117
Simple group      6
Simple module      109
Simplicity of $A_{5}$       68
Simplicity of $A_{n}$       71
Simplicity of PSL(n,F)      60
Socle      136
Socle series      136
Solvable group      95
Special linear group      56
Split extension      26
Stabilizer      29
Staircase group      52
Standard Borel subgroup      41
Standard flag      49
Subflag      52
Subgroup      2
Submodule      109
Subnormal series      92
Successive quotient      89
Supersolvable group      99 105
Syiow’s theorem      64
Sylow p-subgroup      63
Symmetric group      7
System of imprimitivity      36
Tensor product      111
Third isomorphism theorem      13
Thompson, John G.      101 173
Tits system      48
Torsion-free group      2
Totient      15
Transitive action      29
Transposition      8
Transvection      43
Transversal      6
Triply transitive action      71
Trivial subgroup      3
Unipotent matrix      50
Unipotent radical      51
Unipotent subgroup      50
Upper central series      105
Upper triangular matrix      41
Upper unitriangular matrix      49
Virtual character      143
Wedderburn, J.H.M.      120 125 128—133
Weyl group      42 48
Zassenhaus, Hans      13

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