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

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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:

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

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Предметный указатель

Group, p-constrained      20
Group, p-solvable      24
Group, perfect      16
Group, quasisimple      16 53 81
Group, semisimple      16
Group, simple, table of      8—10
Group, solvable      13 16 73—74
Group, sporadic      see “Sporadic group”
Groups in $\mathcal{C}_p$       see “ $\mathcal{C}_p$ -groups”
Groups in $\mathcal{C}_{p'}$       see “ $\mathcal{C}_{p'}$ -groups”
Groups in $\mathcal{G}_p$       see “ $\mathcal{G}_p$ -groups”
Groups in $\mathcal{T}_p$       see “ $\mathcal{T}_p$ -groups”
Groups of $G^{\ast}$ -type ( $G^{\ast}$ a target group), groups of 2-amalgam $G^{\ast}$ -type, $G^{\ast}\in \mathcal{K}^{(4)}$       115
Groups of $G^{\ast}$ -type ( $G^{\ast}$ a target group), groups of 2-central $G^{\ast}$ -type, $G^{\ast}\in \mathcal{K}^{(2)}$ of Lie type      111
Groups of $G^{\ast}$ -type ( $G^{\ast}$ a target group), groups of 2-maximal $G^{\ast}$ -type mod cores, $G^{\ast}\in \mathcal{K}^{(2)\ast}$       111
Groups of $G^{\ast}$ -type ( $G^{\ast}$ a target group), groups of 2-terminal $G^{\ast}$ -type, $G^{\ast}\in \mathcal{K}^{(2)\ast}$       110
Groups of $G^{\ast}$ -type ( $G^{\ast}$ a target group), groups of doubly transitive $G^{\ast}$ -type, $G^{\ast} = L_3(p^n)$ , ,       112
Groups of 3/2-balanced type      120—121
Groups of characteristic 2-type      55 98 116—117
Groups of characteristic p-type      25 116—117
Groups of even type      36 53—55 57—59 81 87 98
Groups of generic type      35—36 55—59 63—68 79 106 118—121
Groups of generic type, groups of $\mathcal{L}_p$ -generic type      57—59 61
Groups of generic type, groups of generic even type      106
Groups of generic type, groups of generic odd type      106
Groups of generic type, groups of semisimple type      121
Groups of generic type, groups of semisimple type, groups of proper semisimple type      121
Groups of GF(2)-type      40—43
Groups of large sporadic type      37—38 61
Groups of Lie type      6ff. 32ff. 45—49
Groups of Lie type as (B,N)-pair      34
Groups of Lie type, Borel subgroup of      33
Groups of Lie type, Bruhat decomposition of      34
Groups of Lie type, Cartan subgroup of      33
Groups of Lie type, Chevalley commutator formula      32
Groups of Lie type, Chevalley group      3
Groups of Lie type, Dynkin diagram of      32 71
Groups of Lie type, generation of      48 65—66
Groups of Lie type, Lie rank of twisted      32
Groups of Lie type, Lie rank of untwisted      32
Groups of Lie type, monomial subgroup of      34
Groups of Lie type, monomial subgroup of, reduced      34
Groups of Lie type, parabolic subgroup of      26 62
Groups of Lie type, rank 1 subgroup of      33 35 71
Groups of Lie type, Ree group      3 10 49 50
Groups of Lie type, root subgroup of      32
Groups of Lie type, root system      32
Groups of Lie type, root system, fundamental system      32
Groups of Lie type, Schur multiplier of      45 48
Groups of Lie type, semisimple element of      51
Groups of Lie type, Steinberg presentation of, relations      33
Groups of Lie type, Steinberg variation      7
Groups of Lie type, Suzuki group      3 10
Groups of Lie type, universal version of      33
Groups of Lie type, universal version of and universal covering group      33
Groups of Lie type, untwisted      see “Chevalley group”
Groups of Lie type, Weyl group of      33 35
Groups of odd order, groups of $\sigma^{\ast}(G)$ -uniqueness type      107
Groups of odd order, groups of odd order uniqueness type      107
Groups of odd order, groups of {p,q}-parabolic type      107—108
Groups of odd type      58—59 81 86
Groups of quasithin type      82 105 114—116
Groups of quasithin type, groups of 2-amalgam type      114—115
Groups of quasithin type, thin subcase      37 41
Groups of restricted even type      58—59 82 90 95 99 102 106
Groups of special type      36—38 58—61 79 103—106 106—108 110—118
Groups of special type, groups of $\mathcal{L}_2$ -special type      58—60 103—104
Groups of special type, groups of $\mathcal{L}_2$ -special type, groups of $\mathcal{LB}_2$ -type      61—63 83 104 110—113 123
Groups of special type, groups of $\mathcal{L}_2$ -special type, groups of $\mathcal{LB}_2$ -type, -subcase      61—63
Groups of special type, groups of $\mathcal{L}_2$ -special type, groups of $\mathcal{LT}_2$ -type      104 114
Groups of special type, groups of $\mathcal{L}_2$ -special type, groups of $\mathcal{LT}_2$ -type, groups of 2-terminal $\mathcal{LT}_2$ -type      114
Groups of special type, groups of $\mathcal{L}_p$ -special type      58—60 105—106
Groups of special type, groups of $\mathcal{L}_p$ -special type, groups of $\mathcal{LC}_p$ -type      105 116—118
Groups of special type, groups of $\mathcal{L}_p$ -special type, groups of $\mathcal{LC}_p$ -type, groups of quasisymplectic $\mathcal{LC}_p$ -type      117
Groups of special type, groups of $\mathcal{L}_p$ -special type, groups of $\mathcal{LC}_p$ -type, groups of wide $\mathcal{LC}_p$ -type      116 133—135
Groups of special type, groups of $\mathcal{L}_p$ -special type, groups of $\mathcal{LT}_p$ -type      106 118
Groups of special type, groups of $\mathcal{L}_p$ -special type, groups of $\mathcal{LT}_p$ -type, groups of p-terminal $\mathcal{LT}_p$ -type      118
Groups of special type, groups of $\sigma^{\ast}(G)$ -uniqueness type      107
Groups of special type, groups of odd order uniqueness type      107
Groups of special type, groups of special even type      105 106 114—118
Groups of special type, groups of special odd type      103—104 106—108 110—114
Groups of special type, groups of {p,q}-parabolic type      107—108
Groups with specified 2-structure, groups of 2-rank at most 2      36 135
Groups with specified 2-structure, groups of 2-rank at most 3      50
Groups with specified 2-structure, groups with semidihedral or wreathed Sylow 2-subgroups      76 136—137
Groups with specified 2-structure, groups with semidihedral or wreathed Sylow 2-subgroups, Brauer group order formula for regular groups      137
Groups with specified 2-structure, groups with semidihedral or wreathed Sylow 2-subgroups, characteristic power      136—137
Hall $\sigma$ -subgroup      25
Hall, M.      11
Hall, P.      16 25
Harada, K.      11 39 89
Hayashi, M.      37
HE      9 11
Holt, D.      89
HS      9 11
Hunt, D.      49
Huppert, B.      46 47
Identification of simple groups      see “Recognition of simple groups”
Inn(X)      13
Int, Int(x)      14
Involution fusion pattern      46 60 62 109 110
Isaacs, I. M.      46 47
Isomorphism question      11
J(P)      26 130
Janko, Z.      11 49
k-balance, weak k-balance      124
k-balanced signalizer functor, weakly k-balanced signalizer functor      125
K-groups      5 12
K-groups, theory of      12 45 48 75—76 138—139
K-proper group      12 75—76 79
Klinger — Mason method      61 105 116—118
Klinger, K.      38 116—117
L(X)      139
Layer      17 (see also “p-layer”)
Leech lattice      11 35
Lie rank (twisted or untwisted)      32
Linear group      18
Local $(k +\dfrac12)$ -balance      126
Local balance      128
Local k-balance, weak local k-balance      126
Local subgroup      19 (see also “p-local subgroup”)
Local subgroup, general structure of      27—28
Lp'-balance      21
Ly      9 11
Lyons, R.      41 48—50 99
m(X)      139
Mason, G.      37—38 41 116—117
Mathieu, E.      11
Maximal subgroup      60 62—63 123
Mc      9 11
McBride, P.      30 49 124
Meierfrankenfeld, U.      130
Meighbor, (y, I)-neighbor      64 119
Modules, failure of factorization      26 130 133
Modules, quadratic      25—26 123 130
Monomial subgroup      34
N-group      38—39 73
Near component      50 96—97 129—131 133
Near component (of Y ): linear, alternating, standard      96 98
Near component 2-local uniqueness subgroup      97
Near component, alternating      96—97 130
Near component, associated module of      96
Near component, linear      96—97 130 131
Near component, standard      98
Near component, type       97
Neighbor      42 64—65 71 119
Neighbor, semisimple      64—65
Neighborhood      55—58 59 63—68 118—120
Neighborhood, $Z_6\times Z_{2^-}$       61 117
Neighborhood, base of      119

Neighborhood, example of      56—57 68—70
Neighborhood, level      66 121
Neighborhood, span of      66—67 121
Neighborhood, vertical      65 76—77 118—120
Neighborhood: level, split, vertical      65 119 120
Niles, R.      39 50
Notation      139
Notation for simple groups      8 9
O'N      9 11
O(X), , $O_{p'}(X)$ , $O_{\pi}(X)$       19
Odd type      58—59 81
Odlyzko, A.      49
Out(X)      29
Outer automorphisms      18
Overall strategy of proof      35—38 42—43
O’Nan, M.      18 45 49 138
p'-core      19; (see also “Core”)
p'-core, elimination      23—24 37 61 120
p'-core, embedding of p'-core of p-local subgroups      21 127—128
p-central element of order p      101
p-central p-element      101
p-component      20
p-component preuniqueness hypothesis      91—92
p-component preuniqueness subgroup      see “Uniqueness subgroups”
p-component uniqueness theorems      30—31 38 53 65 90—92 118
p-component, p-terminal      22ff. 63 108—109
p-component, p-terminal, pumping up to      23 108—109
p-component, solvable      64 109
p-constrained group      20
p-layer      20
p-local subgroup      19
p-local subgroup, embedding of p'-core of      20—21 127—128
p-local subgroup, embedding of p-layer of      21—24 127
p-solvable group      24
p-source      64
p-terminal $\mathcal{G}_p$ -pair      63
p-terminal $\mathcal{LT}_p$ -type      118
p-terminal p-component      23 108
p-uniqueness subgroup      82
Parts of the series      4—5 59 77—78 80
Parts of the series, Part II      38 52—53
Parts of the series, Part III      36
Parts of the series, Part IV      37
Parts of the series, Part V      37 38
perfect central extension      see “Covering group”
Permutation group      18 35
Permutation group, doubly transitive      74 112—113 138
Permutation group, doubly transitive of Suzuki type      95—96
Permutation group, doubly transitive, split (B,N)-pair of rank 1      95—96 112—113 138
Permutation group, highly transitive      11 35
Permutation group, of rank 3      11
Permutation group, representation as      31
Peterfalvi, T.      48—49 96 107 138
Phan, K.-W.      35 71
Presentation      31—35
Presentation of classical groups      35
Presentation of symmetric groups      32 36 68—70
Presentation, Steinberg presentation of groups of Lie type      32 33 36 51 118
Presentation, Steinberg presentation of groups of Lie type, a la Curtis — Tits      34 67 70
Presentation, Steinberg presentation of groups of Lie type, a la Gilman — Griess      35 67 71
proper 2-generated core      89
proper semisimple type      121
Pumpup      22 127
Pumpup as $\mathcal{C}_p$ , $\mathcal{T}_p$ , or $\mathcal{G}_p$ -group      103 114
Pumpup, diagonal, proper, trivial, or vertical      22 127
Pumpup: vertical, trivial, diagonal, proper      22 127
Quadratic -module      25
Quadratic chief factor      26
Quasisimple group      16 53 81
Quasisymplectic type      117
Quasithin      5 37 41 43 60—61 82 105 114—116
Quasithin, quasithin type, quasithin case      60 82
Recognition of simple groups      31—35
Recognition of simple groups, alternating groups      32
Recognition of simple groups, groups of Lie type      32—35 42 49 137—138
Recognition of simple groups, recognition of symmetric groups      68—70
Recognition of simple groups, sporadic groups      35
Reduced monomial subgroup      34
Ree group      10
Ree groups      3 10 49 50
Ree, R.      10
Regular      136
Restricted even type      95
Root subgroup, root system      32
Rowley, P.      37
Ru      9 11
S(G)      29
Schreier property      21 24 29
Schreier, O.      21
Schur multiplier      18 45 48 139
Schur, I.      17
Scott, L.      18
Section      12
Seitz, G.      48
Semisimple group      16
Semisimple neighbor      64
Semisimple type      121
Sibley, D.      48
Signalizer functor      29—30 124ff.
Signalizer functor method      29—30 36—38 41 60 64—65 104—105 116 118 120 128—129
Signalizer functor, closed      124
Signalizer functor, closure      30 124
Signalizer functor, complete      124
Signalizer functor, k-balanced, weakly k-balanced      124—126
Signalizer functor, solvable      124
Signalizer functor, trivial      124 128
Signalizer functor: A-signalizer functor, solvable, closed, complete      124
Simple group      13
Simple groups, table of      8—10
Simplicity criteria      29—31
Sims, C.      39 45
Sims, conjecture      74
Smith, F.      41
Smith, S.      41
Solomon, R.      35 39 53
Solvable component, solvable p-component      109
Solvable group      13
Span of $\mathcal{N}$       66 121
Special even type      105
Special odd type      103
Special, special type      58
Spor      81
Sporadic groups      3 6 9 11 87 100
Sporadic groups as $\mathcal{G}_p$ -group      103
Sporadic groups as target group      77 87
Sporadic groups, background properties of      44—48 50
Sporadic groups, existence and uniqueness of      46—47 50 72
Sporadic groups, individual groups, Baby Monster       11 38 87 100
Sporadic groups, individual groups, Conway groups $C_{o_1}=\dot 1$ , $C_{o_2}=\dot 2$ , $C_{o_3}=\dot 3$       11 38 42 72 87 100
Sporadic groups, individual groups, Fischer 3-transposition groups $F_{i_{22}}$ , $F_{i_{23}}$ , $F_{i'_{24}}$       11 38 87 100
Sporadic groups, individual groups, Fischer — Griess Monster       3 11 38 42 47 61 72 87 100
Sporadic groups, individual groups, Harada — Norton       11 67—68 87 100
Sporadic groups, individual groups, Held He = HHM      11 87 100
Sporadic groups, individual groups, Higman — Sims HS      11 87 100
Sporadic groups, individual groups, Janko , , ,       3 11 87 100
Sporadic groups, individual groups, Lyons — Sims Ly      11 45 87 100
Sporadic groups, individual groups, Mathieu $M_{11}$ , $M_{12}$ , $M_{22}$ , $M_{23}$ , $M_{24}$       11 42 46 72 87 100
Sporadic groups, individual groups, McLaughlin Mc      11 87 100
Sporadic groups, individual groups, O’Nan-Sims O'N      11 87 100
Sporadic groups, individual groups, Rudvalis Ru      11 87 100
Sporadic groups, individual groups, Suzuki Suz      11 87 100
Sporadic groups, individual groups, Thompson       11 87 100
Standard component      53
Standard form problems      38
Standard preuniqueness subgroup      91
Steinberg presentation, relations      32—33
Steinberg variation      10
Steinberg, R.      3 7 10 17 45 47 48
Stellmacher, B.      37 50
Strong p-uniqueness subgroup      52 94

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