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



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Ќазвание: The Classification of the Finite Simple Groups

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

язык: en

–убрика: ћатематика/јлгебра/“еори€ групп/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2000

 оличество страниц: 166

ƒобавлена в каталог: 12.12.2004

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Group, p-constrained      20
Group, p-solvable      24
Group, perfect      16
Group, quasisimple      16 53 81
Group, semisimple      16
Group, simple, table of      8Ч10
Group, solvable      13 16 73Ч74
Group, sporadic      see УSporadic groupФ
Groups in $\mathcal{C}_p$      see У$\mathcal{C}_p$-groupsФ
Groups in $\mathcal{C}_{p'}$      see У$\mathcal{C}_{p'}$-groupsФ
Groups in $\mathcal{G}_p$      see У$\mathcal{G}_p$-groupsФ
Groups in $\mathcal{T}_p$      see У$\mathcal{T}_p$-groupsФ
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, $G^{\ast} = L_3(p^n)$, $U_3(p^n)$, $^2G_2(3^n)$      112
Groups of 3/2-balanced type      120Ч121
Groups of characteristic 2-type      55 98 116Ч117
Groups of characteristic p-type      25 116Ч117
Groups of even type      36 53Ч55 57Ч59 81 87 98
Groups of generic type      35Ч36 55Ч59 63Ч68 79 106 118Ч121
Groups of generic type, groups of $\mathcal{L}_p$-generic type      57Ч59 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      40Ч43
Groups of large sporadic type      37Ч38 61
Groups of Lie type      6ff. 32ff. 45Ч49
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 65Ч66
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 УChevalley groupФ
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      107Ч108
Groups of odd type      58Ч59 81 86
Groups of quasithin type      82 105 114Ч116
Groups of quasithin type, groups of 2-amalgam type      114Ч115
Groups of quasithin type, thin subcase      37 41
Groups of restricted even type      58Ч59 82 90 95 99 102 106
Groups of special type      36Ч38 58Ч61 79 103Ч106 106Ч108 110Ч118
Groups of special type, groups of $\mathcal{L}_2$-special type      58Ч60 103Ч104
Groups of special type, groups of $\mathcal{L}_2$-special type, groups of $\mathcal{LB}_2$-type      61Ч63 83 104 110Ч113 123
Groups of special type, groups of $\mathcal{L}_2$-special type, groups of $\mathcal{LB}_2$-type, $SL_2(q)$-subcase      61Ч63
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      58Ч60 105Ч106
Groups of special type, groups of $\mathcal{L}_p$-special type, groups of $\mathcal{LC}_p$-type      105 116Ч118
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 133Ч135
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 114Ч118
Groups of special type, groups of special odd type      103Ч104 106Ч108 110Ч114
Groups of special type, groups of {p,q}-parabolic type      107Ч108
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 136Ч137
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      136Ч137
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 УRecognition of simple groupsФ
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 75Ч76 138Ч139
K-proper group      12 75Ч76 79
Klinger Ч Mason method      61 105 116Ч118
Klinger, K.      38 116Ч117
L(X)      139
Layer      17 (see also Уp-layerФ)
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 Уp-local subgroupФ)
Local subgroup, general structure of      27Ч28
Lp'-balance      21
Ly      9 11
Lyons, R.      41 48Ч50 99
m(X)      139
Mason, G.      37Ч38 41 116Ч117
Mathieu, E.      11
Maximal subgroup      60 62Ч63 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      25Ч26 123 130
Monomial subgroup      34
N-group      38Ч39 73
Near component      50 96Ч97 129Ч131 133
Near component (of Y ): linear, alternating, standard      96 98
Near component 2-local uniqueness subgroup      97
Near component, alternating      96Ч97 130
Near component, associated module of      96
Near component, linear      96Ч97 130 131
Near component, standard      98
Near component, type $G_2(3^n)$      97
Neighbor      42 64Ч65 71 119
Neighbor, semisimple      64Ч65
Neighborhood      55Ч58 59 63Ч68 118Ч120
Neighborhood, $Z_6\times Z_{2^-}$      61 117
Neighborhood, base of      119
Neighborhood, example of      56Ч57 68Ч70
Neighborhood, level      66 121
Neighborhood, span of      66Ч67 121
Neighborhood, vertical      65 76Ч77 118Ч120
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), $O_p(X)$, $O_{p'}(X)$, $O_{\pi}(X)$      19
Odd type      58Ч59 81
Odlyzko, A.      49
Out(X)      29
Outer automorphisms      18
Overall strategy of proof      35Ч38 42Ч43
OТNan, M.      18 45 49 138
p'-core      19; (see also УCoreФ)
p'-core, elimination      23Ч24 37 61 120
p'-core, embedding of p'-core of p-local subgroups      21 127Ч128
p-central element of order p      101
p-central p-element      101
p-component      20
p-component preuniqueness hypothesis      91Ч92
p-component preuniqueness subgroup      see УUniqueness subgroupsФ
p-component uniqueness theorems      30Ч31 38 53 65 90Ч92 118
p-component, p-terminal      22ff. 63 108Ч109
p-component, p-terminal, pumping up to      23 108Ч109
p-component, solvable      64 109
p-constrained group      20
p-layer      20
p-local subgroup      19
p-local subgroup, embedding of p'-core of      20Ч21 127Ч128
p-local subgroup, embedding of p-layer of      21Ч24 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      4Ч5 59 77Ч78 80
Parts of the series, Part II      38 52Ч53
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 УCovering groupФ
Permutation group      18 35
Permutation group, doubly transitive      74 112Ч113 138
Permutation group, doubly transitive of Suzuki type      95Ч96
Permutation group, doubly transitive, split (B,N)-pair of rank 1      95Ч96 112Ч113 138
Permutation group, highly transitive      11 35
Permutation group, of rank 3      11
Permutation group, representation as      31
Peterfalvi, T.      48Ч49 96 107 138
Phan, K.-W.      35 71
Presentation      31Ч35
Presentation of classical groups      35
Presentation of symmetric groups      32 36 68Ч70
Presentation, Steinberg presentation of groups of Lie type      32 33 36 51 118
Presentation, Steinberg presentation of groups of Lie type, a la Curtis Ч Tits      34 67 70
Presentation, Steinberg presentation of groups of Lie type, a la Gilman Ч 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 $F_pX$-module      25
Quadratic chief factor      26
Quasisimple group      16 53 81
Quasisymplectic type      117
Quasithin      5 37 41 43 60Ч61 82 105 114Ч116
Quasithin, quasithin type, quasithin case      60 82
Recognition of simple groups      31Ч35
Recognition of simple groups, alternating groups      32
Recognition of simple groups, groups of Lie type      32Ч35 42 49 137Ч138
Recognition of simple groups, recognition of symmetric groups      68Ч70
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      29Ч30 124ff.
Signalizer functor method      29Ч30 36Ч38 41 60 64Ч65 104Ч105 116 118 120 128Ч129
Signalizer functor, closed      124
Signalizer functor, closure      30 124
Signalizer functor, complete      124
Signalizer functor, k-balanced, weakly k-balanced      124Ч126
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      8Ч10
Simplicity criteria      29Ч31
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      44Ч48 50
Sporadic groups, existence and uniqueness of      46Ч47 50 72
Sporadic groups, individual groups, Baby Monster $F_2=BM$      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 Ч Griess Monster $F_1=M$      3 11 38 42 47 61 72 87 100
Sporadic groups, individual groups, Harada Ч Norton $F_5=HN$      11 67Ч68 87 100
Sporadic groups, individual groups, Held He = HHM      11 87 100
Sporadic groups, individual groups, Higman Ч Sims HS      11 87 100
Sporadic groups, individual groups, Janko $J_1$, $J_2 = HJ$, $J_3 = HJM$, $J_4$      3 11 87 100
Sporadic groups, individual groups, Lyons Ч 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, OТNan-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 $F_3=Th$      11 87 100
Standard component      53
Standard form problems      38
Standard preuniqueness subgroup      91
Steinberg presentation, relations      32Ч33
Steinberg variation      10
Steinberg, R.      3 7 10 17 45 47 48
Stellmacher, B.      37 50
Strong p-uniqueness subgroup      52 94
1 2 3
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