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Gorenstein D., Lyons R., Solomon R. — The Classification of the Finite Simple Groups
Gorenstein D., Lyons R., Solomon R. — The Classification of the Finite Simple Groups



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Название: The Classification of the Finite Simple Groups

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

Язык: en

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
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Предметный указатель
$(k +\dfrac12)$-balance      125
$(S)L_n(q)$      101
$2A_n$, $(2)A_n$      60 100
$2D_n(q)$      101
$3U_4(3)$      101
$4L_3(4)$      101
$A\bar{K}$ (central extension)      101
$A_n$      6 8
$A_n(q)$, $^2A_n(q)$, $A_n^+(q)$, $A_n^-(q)$      7 8
$B_n(q)$, $^2B_2(2^n)$      7 8 10
$B_p$-property      24 28 40—41 62 123 127
$B_p$-property, partial      30 36 42 64
$B_{p'}(X)$      24
$C_n(q)$      7 8
$C_x$      63
$C_X(A/B)$      22
$C_X(V)$      14
$C_Y$      139
$C_{o_1}$, $C_{o_2}$, $C_{o_3}$      9 11
$D_n(q)$, $^2D_n(q)$, $^3D_4(q)$, $D_n^+(q)$, $D_n^-(q)$      7 8 10
$E_n(q)$, $^2E_6(q)$, $E_6^+(q)$, $E_6^-(q)$      7 8 10
$E_{p^n}$      14
$F^{\ast}(X)$      17
$F_1$, $F_2$, $F_3$, $F_5$      9 11
$F_4(q)$, $^2F_4(2^n)$, $^2F_4(2)'$      7 8 10
$F_{i_{22}}$, $F_{i_{23}}$, $F_{i'_{24}}$      9 11
$GL_n(q)$      6
$GU_n(q)$      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
$G_0(N)$      66 121
$G_2(q)$, $^2G_2(3^n)$      7 8 10
$G_{\alpha}$, $G_{\alpha}^{\ast}$      71
$J_1$, $J_2$, $J_3$, $J_4$      9 11
$LB_2$-type      104
$LC_p$-type      105
$LC_p$-uniqueness subgroup      94
$LT_p$-type      104
$L^{\ast}$-balance      127
$L^{\ast}_{p'}$-balance      127—128
$L_n(q)=L_n^+(q)$      6 8
$L_n^-(q)$      8
$L_p$-generic type      57—58
$L_p$-special type, $L_2$-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
$m_p(A)$      30 81
$M_{11}$, $M_{12}$, $M_{22}$, $M_{23}$, $M_{24}$      9 11
$m_{2,p}(G)$      135
$N_X(Q)$      19
$N_Y$      139
$O^p(X)$, $O^{p'}(X)$, $O^{\pi}(X)$      19
$O_{p'p}(X)$      24
$PSL_n(q)$      6 8
$PSp_n(q)$      7 8
$PSU_n(q)$      7 8
$P\Omega_n^{\pm}(q)$, $P\Omega_n(q)$, $(P)\Omega_n(q)$      7 8 101
$SL_n(q)$      6
$SU_n(q)$      7
$Sz(2^n)$      8 10
$U_n(q)$      8
$Z_6\times Z_2$-neighborhood      117
$Z_p$      6 8
$[A_1\times A_2]\bar{K}$ (central extension)      101
$[I_1]$, $[I_2]$, $[I_A]$, $[I_G]$, $[II_A]$, $[II_G]$, $[II_P]$, $[II_S]$      4—5
$[X]L_3(4)$      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 $(M_1,M_2;S)$      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 $A_n$      6 32 36
Alternating group $A_n$ 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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