Gorenstein D., Lyons R., Solomon R. - The Classification of the Finite Simple Groups :: Электронная библиотека попечительского совета мехмата МГУ

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Название: The Classification of the Finite Simple Groups

Авторы: Gorenstein D., Lyons R., Solomon R.

Язык:

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 166

Добавлена в каталог: 12.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(k +\dfrac12)$ -balance      125
      101
,       60 100
      101
      101
      101
$A\bar{K}$ (central extension)      101
      6 8
, , ,       7 8
,       7 8 10
-property      24 28 40-41 62 123 127
-property, partial      30 36 42 64
$B_{p'}(X)$       24
      7 8
      63
      22
      14
      139
$C_{o_1}$ , $C_{o_2}$ , $C_{o_3}$       9 11
, , , ,       7 8 10
, , ,       7 8 10
$E_{p^n}$       14
$F^{\ast}(X)$       17
, , ,       9 11
, ,       7 8 10
$F_{i_{22}}$ , $F_{i_{23}}$ , $F_{i'_{24}}$       9 11
      6
      7
$G\approx G^{\ast}$       109-121
$G\approx G^{\ast}$ , $G^{\ast}$ of Lie type of large Lie rank      116 121
$G\approx G^{\ast}$ , $G^{\ast}$ of Lie type of small Lie rank, of characteristic 2      95-96 115
$G\approx G^{\ast}$ , $G^{\ast}$ of Lie type of small Lie rank, of characteristic 2 and Lie rank 1      95-96
$G\approx G^{\ast}$ , $G^{\ast}$ of Lie type of small Lie rank, of odd characteristic      110 112 113
$G\approx G^{\ast}$ , $G^{\ast}$ sporadic      109
$G\approx G^{\ast}$ , $G^{\ast}=A_n$ , $n\geq 13$       121
$G\approx G^{\ast}$ , $G^{\ast}=A_n$ , $n\leq 12$       109 114
$G^{\ast}$       27
      66 121
,       7 8 10
$G_{\alpha}$ , $G_{\alpha}^{\ast}$       71
, , ,       9 11
-type      104
-type      105
-uniqueness subgroup      94
-type      104
$L^{\ast}$ -balance      127
$L^{\ast}_{p'}$ -balance      127-128
      6 8
      8
-generic type      57-58
-special type, -special type      58 103
$L_{p'}$ -balance      21 127-128
$L_{p'}$ -balance, analogue for near components      96
$L_{p'}$ -balance, analogue for two primes      134
$L_{p'}(X)$       20
$L_{p'}^{\ast}(X)$       127
$M\rightsquigarrow N$       123
      30 81
$M_{11}$ , $M_{12}$ , $M_{22}$ , $M_{23}$ , $M_{24}$       9 11
$m_{2,p}(G)$       135
      19
      139
, $O^{p'}(X)$ , $O^{\pi}(X)$       19
$O_{p'p}(X)$       24
      6 8
      7 8
      7 8
$P\Omega_n^{\pm}(q)$ , $P\Omega_n(q)$ , $(P)\Omega_n(q)$       7 8 101
      6
      7
      8 10
      8
$Z_6\times Z_2$ -neighborhood      117
      6 8
$[A_1\times A_2]\bar{K}$ (central extension)      101
, , , , , , ,       4-5
      101
$\bar{X}$ , $\hat{X}$ , $X^{\ast}$       139
$\Delta_X(B)$       64 124
$\Gamma$ , $\Gamma(\alpha)$       132
$\gamma(G)$       66
$\Gamma^o_{P,2}(X)$       82
$\Gamma_{P,k}(X)$       82
$\hat{L}_{p'}(X)$       21
$\mathbf{F}_q$       6
$\mathcal{A}(T)$       130
$\mathcal{A}lt$       81
$\mathcal{B}_2$ , $\mathcal{B}_2$ -group      60 104
$\mathcal{B}_{\ast}^p(G)$       116
$\mathcal{CH}_p$       101
$\mathcal{C}hev$ , $\mathcal{C}hev(p)$       81
$\mathcal{C}_p$       102
$\mathcal{C}_p$ , $\mathcal{C}_p$ -group      100
$\mathcal{C}_p$ -groups      54 57 81 99-101
$\mathcal{C}_p$ -groups as pumpups      101-102
$\mathcal{C}_{p'}$ , $\mathcal{C}_{p'}$ -group      100
$\mathcal{C}_{p'}$ -groups      95 100
$\mathcal{E}(X)$ , $\mathcal{E}_k(X)$       139
$\mathcal{E}^p(X)$ , $\mathcal{E}^p_k(X)$       124
$\mathcal{FM}9$       95
$\mathcal{G}_p$       102
$\mathcal{G}_p$ -groups      57-58 63 103
$\mathcal{H}_p$ , $\hat{\mathcal{H}}_p$ , $\mathcal{H}_p^{\ast}$       101
$\mathcal{I}(X)$       139
$\mathcal{I}^0_p(G)$ , $\mathcal{I}^0_2(G)$       55 103
$\mathcal{I}_p(G)$       55 81
$\mathcal{J}_0(p)$ , $\mathcal{J}_1(p)$ , $\mathcal{J}_2(p)$       102
$\mathcal{K}$       53 81
$\mathcal{K}$ -group      12
$\mathcal{K}$ -proper      12
$\mathcal{K}^{(2)\ast}$       110
$\mathcal{K}^{(i)}$ , i=0,...,7      86
$\mathcal{K}_p$       53 81
$\mathcal{LT}_2$ -type      104
$\mathcal{L}(q)$       7
$\mathcal{L}(X)$       139
$\mathcal{L}_p(G)$       53 81
$\mathcal{L}_p(G;A)$       126
$\mathcal{L}_p^0(G)$       55 103
$\mathcal{M}(S)$ , $\mathcal{M}_1(S)$       58. 60 82
$\mathcal{N}$       65
$\mathcal{N}(M)$ , $\mathcal{N}^{\ast}(M)$       97
$\mathcal{Q}(M_p)$       98
$\mathcal{S}^p(X)$ , $\mathcal{S}^p_n(X)$       94
$\mathcal{T}_p$       102
$\mathcal{T}_p$ -groups      57 102-103 129
$\mathcal{T}_p$ -groups as pumpups      101-103
$\mathcal{Z}$ , $\mathcal{Z}_X$       88
$\Omega_1(B)$       26
$\Omega_8^-(3)$ -type      117
$\Phi(X)$       18
$\pi$       32
$\pi$ , $\pi'$       19
$\sigma$ -subgroup      25
$\sigma(G)$       37 82
$\sigma^{\ast}(G)$       107
$\sigma_0(G)$       58 83
$\sigma_{\mathcal{G}}(G)$       120
$\sigma_{\mathcal{T}}(G)$       118
$\sim$       90
$\succeq$       97
$\sum$ , $\sum^+$ , $\sum^-$       32
$\sum_n$       6
$\Theta$ , $\Theta(C_G(a))$ , $\Theta(G;A)$ , $\Theta_{k+\frac12}$ , $\Theta_{k+\frac12}(G;A)$       30 124-125
(B, N)-pair      34
(B, N)-pair, split      34
(B, N)-pair, split, recognition of rank 1      36-37 39 49 50 63 113 138
(B, N)-pair, split, recognition of rank 2      37 63 111 113 115 137-138
(B,N)-pair, split (B,N)-pair      34
(y, I)-neighborhood      65

2-amalgam $G^{\ast}$ -type      115
2-amalgam type, 2-amalgam type       114-115
2-central $G^{\ast}$ -type      111
2-central involution      88
2-local p-rank      135
2-maximal $G^{\ast}$ -type mod cores      111
2-terminal $G^{\ast}$ -type      110
2-terminal $\mathcal{LT}_2$ -type      114
2-uniqueness subgroup      82
3/2-balance      64
3/2-balanced functor      43 64-65
3/2-balanced type      120
A-composition factor, length, series      13
Algebraic automorphism      118 121
Almost p-constrained p-component preuniqueness subgroup      93
Almost simple group      18
Almost strongly p-embedded subgroup      94 (see also 'Uniqueness subgroups')
Alperin, J.      39 41
Alternating group       6 32 36
Alternating group as $\mathcal{C}_2$ , $\mathcal{T}_2$ or $\mathcal{G}_2$ -group      103
Amalgam method      5-6 26 39 41 43 60-61 105 131-133
Amalgam method, associated graph      132-133
Amalgam method: $A_{\alpha}$ , $Q_{\alpha}$ , $S_{\alpha}$ , $X_{\alpha}$ , $Z_{\alpha}$       131-132
Artin, E.      11
Aschbacher $\chi$ -block      39 41 53
Aschbacher, M.      18 30 37 39-43 45-48 50 53 89 99 125 129 130
Associated $(k +\dfrac12)$ -balanced functor      125
Associated module of a near component      96
Atlas of Finite Groups      45 50 139
Background references      47-50 140
Background results      59 63 79 87 104 118
Background Results, Background References      44-50
Background results, listed      44-50
Balance, k-balance      see 'Group' (also see 'Signalizer functor')
Bar convention      18 139
Base of a neighborhood      119
Baumann, B.      39 131
Bender method      30 38 43 60 62 104 110 123 134
Bender, H.      16-17 48-50 123
Blackburn, N.      46 47
Bombieri, E.      49
Borel subgroup      34
Borel, A.      25
Brauer - Suzuki theory of exceptional characters      38 135
Brauer, R.      51
Brauer, theory of blocks      38 46 50 62
Brauer, theory of blocks, defect groups of 2-rank at most 3      50
Bruhat decomposition: B, H, N, R, U, V, $X_{\alpha}$ , W, $h_{\alpha}(t)$ , $n_{\alpha}(t)$       33 34
Building      34 73 138
Burnside, W.      29-30
C(G,S)      90
C(K,x)      22
Cartan subgroup      33
Carter, R.      45 47
Centralizer of element of odd prime order p      35 41 42 51 54-56
Centralizer of element of prime order p      108
Centralizer of involution      11 27ff. 35 39 41-43 51 52 54 61-62
Centralizer of involution pattern      46 59 77 109-110
Centralizer of semisimple element      51 54-56
Character theory      31 46 50 60 62 104 108 135-137
Character theory, ordinary vs. modular      50
Characteristic 2-core      90
Characteristic p-type      25
Characteristic power      136
Characteristic subgroup      16
Chevalley commutator formula      32-33
Chevalley group      7
Chevalley groups      see 'Groups of Lie type'
Chevalley, C.      3
Chief factor, series      13-14
Classical group      6
Classical groups      6ff. (see also 'Groups of Lie type')
Classification Grid      79 83 85 99-121
Classification Theorem      see 'Theorems'
Classification Theorem, Theorems $\mathcal{C}_1-\mathcal{C}_7$       104-106
Component      17 51 81
Component, solvable      51 67 109
Component, standard      53 91-92
Component, terminal      23 42 53 81 90-92 108
Composition factor, A-composition factor, length, series      13
Composition factor, length, series      12
Computer      35 45 68
Control of (strong) G-fusion (in T)      87
Control of 2-locals      129
Control of fusion      87 122
Control of rank 1 (or rank 2) fusion      91
Control of rank 1 or 2 fusion      91-92
Conway, J.      11
Core      20 (see also 'p'-core')
Core, elimination      40 43 60 110-111
Covering group      16
Covering group, notation for      101
Covering group, universal      17 33
Curtis, C.      35
Das, K. M.      35 71
Delgado, A.      37
Dickson, L.      7
Dieudonne, J.      47
Double transitivity of Suzuki type      95-96
Doubly transitive $G^{\ast}$ -type      112
Doubly transitive of Suzuki type      95-96
E(X)      17
Enguehard, M.      49-50
Even type      55 81
Expository references      47 141-146
Extremal conjugation      122
F(X)      16
Failure of factorization module      26
Feit, W.      46 47 48 107-108
Finkelstein, L.      35
Fischer, B.      11 39-40
Fischer, transpositions      11 39
Fitting length, series      19
Fitting subgroup      16
Fitting subgroup, generalized Fitting subgroup      17 123
Foote, R.      5 38 53 98
Four-group      39
Frattini subgroup      18
Frobenius group      107
Frobenius, G.      29
Frohardt, D.      35
Fusion      29 60 62 63 104 120 122
Fusion, extremal conjugation      122
G(q), $\hat{G}(q)$       32-33
General local group theory      45-48
Generalized Fitting subgroup      17 123
Generic even type      106
Generic odd type      106
Generic, generic type      58 106
Geometry associated with a finite group      35 73-74
Gilman, R.      35 39 41
Glauberman, G.      21 38 39 48-50 124 130
Goldschmidt, D.      39 43 49 125
Gomi, K.      37
Gorenstein, D.      29 38 39 41 46 47-50 99 124 126 127
Griess, R. L.      17 35 41 45
Group of Lie type      see 'Groups of Lie type'
Group order formulas      50 135-137
Group, $\mathcal{K}$ -proper      12 21
Group, almost simple      18
Group, alternating      see 'Alternating group'
Group, covering      16
Group, covering, notation for      101
Group, covering, universal      17 33
Group, k-balanced      124-125 129
Group, k-balanced, $(k +\dfrac12)$ -balanced      125 129
Group, k-balanced, locally balanced      128
Group, k-balanced, locally k-balanced, $k +\dfrac12$ -balanced      126
Group, k-balanced, weakly k-balanced, weakly locally k-balanced      124 126
Group, nilpotent      15-16

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