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| Авторизация |
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| Alperin J.L., Bell R.B. — Groups and Representations, Vol. 0 |
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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  159
Character table of  156
Character table of  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  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 68
Simplicity of  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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