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| Aschbacher M. — Finite Group Theory |
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| Предметный указатель |
Normal series, A-invariant 20
Normal series, factors 23
Normal series, length 20
normalizer 3
O(V,f), O(V,Q) 78
Odd Order Theorem 259
Orbit 13
Orbital 54
Orbital, diagonal 54
Orbital, paired 59
Orbital, self paired 59
Ordinary Chevalley group 252
Orthogonal group 88
Orthogonality relations 183
Out(G) 11
Outer automorphism group 11
p',  5
p-group 5
p-group, elementary abelian 5
p-group, extraspecial 108
p-group, modular 106
p-group, special 108
p-group, symplectic type 109
p-rank 5
p-rank, 2-local 260
Parabolic subgroup 220
Partition, G-invariant 18
Partition, nontrivial 18
Path 8
Path, length 8
Pdim 43
Permutation group 53
Permutation representation 9
Permutation representation, by conjugation 15
Permutation representation, by right multiplication 15
Permutation representation, m-transitive 56
Permutation representation, primitive 18
Permutation representation, rank 54
Permutation representation, regular 56
Permutation representation, semiregular 56
Permutation representation, transitive 14
Permutation representation, transitive constituents 16
Permutation, even 54
Permutation, odd 54
Phillip Hall's Theorem 71
Presentation 140
Projective general linear group 44
Projective geometry 43
Projective geometry, dimension 43
Projective geometry, hyperplane 44
Projective geometry, lines 44
Projective geometry, points 44
Projective special linear group 44
PSL(V), PGL(V) 44
Quaternion group 107
Rad(V) 76
Rainy Day Lemma 215
Reflection 93
Reflection, center 93
Representation 9
Representation, equivalence 9
Representation, faithful 9
Representation, quasiequivalence 9
Residue 8
Root group 250
Root system 148
Root system, closed subset 253
Root system, ideal 253
Root system, ordering 149
Root system, positive system 149
Root system, simple system 149
Root system, Weyl group 148
Root, long 252
Root, short 252
S(A, G,  ) 30
Scalar matrix 44
Scalar transformation 44
Schreier conjecture 160
Schur multiplier 167
Schur — Zassenhaus theorem 70
Schur's lemma 38
Semidihedral group 107
Semidirect product 30
| sgn(Q), sgn(V) 86 87
Signalizer functor 228
Signalizer functor, complete 228
Signalizer functor, solvable 228
Signalizer functor, solvably complete 228
Similarity 78
simplex 208
Sims conjecture 176
SL(V), PG(V) 45
SO(V), O(V),  88 89
Soc(V) 38 158
Solvable Signalizer Functor Theorem 228
Sp(F), Sp(V) 88
Space, hyperbolic 81
Space, orthogonal 78
Space, symplectic 78
Space, unitary 78
Special Clifford group 97
Special linear group 44
Special orthogonal group 89
Special unitary group 89
Spinor norm 98
Splitting field 123
Sporadic group 253
Stabilizer, global 14
Stabilizer, pointwise 14
Stable subset 163
Standard Form Theorem 263
Standard subgroup 259
Subgroup see also "Hall -subgroup" "Sylow
Subgroup, characteristic 25
Subgroup, commutator 27
Subgroup, derived 27
Subgroup, generated by a set 2
Subgroup, minimal normal 25
Subgroup, p-local 156
Subgroup, regular normal 56
Subgroup, strongly embedded 247
Subgroup, subnormal 20
Subspace, nondegenerate 77
Subspace, totally isotropic 77
Subspace, totally singular 78
Suzuki group 252
Sylow p-subgroup 19
Sym(X) 9
Symplectic group 88
Tensor product 118
Tensor, fundamental 118
Thompson  Lemma 112
Thompson Factorization Theorem 166
Thompson Order Formula 244
Thompson subgroup 162
Three Subgroup Lemma 26
TI-set 189
Tits system 217
Tits system, saturated 226
Tr, det 44
TRANSFER 198
Transposition 53
Transvection 45
Transvection, axis 45
Transvection, center 45
Trichotomy theorem 264
Twisted Chevalley group 252
U(G,V) 65
Unbalanced Group Theorem 262
Unipotent radical 256
Unitary group 88
V* 47
Vector, isotropic 77
Vector, singular 78
Vertex 8
Weakly closed subset 199
Witt property 81
Word 138
Word, length 138
Wreath product 33
XG 13
XY 4
Z(G) 5
[X,Y,Z] 26
[X,Y] 26 45
|G:H| 3
|G| 2
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