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

Strongly closed subgroup      61
Strongly closed type p-component preuniqueness subgroup      93
Strongly embedded subgroup      see “Uniqueness subgroups”
Strongly p-embedded subgroup      see “Uniqueness subgroups”
Strongly Z-embedded subgroup      see “Uniqueness subgroups”
Stroth, G.      5 37 38 43 53 98—99 107 130
Subterminal (x,K)-pair      64
Subterminal pair      64—66
Suz      9 11
Suzuki group      10
Suzuki groups       3 10
Suzuki, M.      10 38 46 47 49
Symmetric group $\sum_n$       6
Symplectic pair      117
Symplectic pair, faithful, of $\Omega_8^-(3)$ -type, trivial      117
Symplectic pair: faithful, trivial      117
Symplectic type      116
Symplectic type 2-group      116
Tanaka, Y.      37
Target group $(G^{\ast})$       27 54—55 86—87
Target group $(G^{\ast})$ in $K^{(0)}$       89
Target group $(G^{\ast})$ of Lie type      76– 77
Target group $(G^{\ast})$ of Lie type of large Lie rank      63—68 71 76
Target group $(G^{\ast})$ of Lie type of Lie rank 1      77 110—113
Target group $(G^{\ast})$ of Lie type of small Lie rank      77 110—116
Target group $(G^{\ast})$ of Lie type, $L_3^{\pm}(q)$ , , , , $L_4^{\pm}(q)$ , q odd      61—63
Target group $(G^{\ast})$ , , $n\geq 13$       63—68 76–
Target group $(G^{\ast})$ , , $n\geq 13$ , $\sum_n$       68—70
Target group $(G^{\ast})$ , , $n\leq 12$       77 111—112 114—116
Target group $(G^{\ast})$ , quasithin      77
Target group $(G^{\ast})$ , sporadic      77 87
Target group $(G^{\ast})$ , sporadic, large sporadic      116—117
Target group $(G^{\ast})$ , the 8 families $\mathcal{K}^{(i)}$ $(0\leq i\leq 7)$       86
Terminal component      23 81
Theorems , ,       92
Theorems $\mathcal{C}_1–\mathcal{C}_7$       104–106
Theorems, Alperin — Brauer — Gorenstein — Walter classification of groups of 2-rank 2      39 41
Theorems, Alperin —Goldschmidt conjugation theorem      97 122
Theorems, Aschbacher classical involution theorem      41—43
Theorems, Aschbacher proper 2-generated core theorem      89
Theorems, Aschbacher uniqueness case theorem      43 92
Theorems, Aschbacher — Bender — Suzuki strongly Z-embedded subgroup theorem      88
Theorems, Aschbacher — Gilman component theorem      39 40 52 75
Theorems, Aschbacher — Gilman component theorem, generalized to odd primes      75—76
Theorems, Baumann — Glauberman — Niles theorem      50 130—131
Theorems, Baumann — Glauberman — Niles theorem, revision of      50
Theorems, Bender $F^{\ast}$ -theorem      17 138
Theorems, Bender uniqueness theorem      123
Theorems, Bender — Suzuki strongly embedded subgroup theorem      30—31 33 36 38 52
Theorems, Bender — Suzuki strongly embedded subgroup theorem for K-proper groups      75
Theorems, Bender — Thompson signalizer lemma      116
Theorems, Brauer — Suzuki quaternion theorem      52
Theorems, Burnside -theorem      30
Theorems, classification theorem      6 79
Theorems, classification theorem, comparison of new and old proofs      41–44 55 63 72 74–76 98
Theorems, classification theorem, four-part division      58–59
Theorems, classification theorem, main logic      106
Theorems, classification theorem, stages of the proof      61 106–121
Theorems, Curtis — Tits theorem      35 63 67 113 115
Theorems, Curtis — Tits theorem, variations for classical groups      35 63 113 115
Theorems, Feit — Thompson theorem      see “Odd order theorem”
Theorems, Fong — Seitz classification of split (B, N)-pairs of rank 2      63 138
Theorems, Gilman — Griess recognition theorem for groups of Lie type      35 67 71
Theorems, Glauberman $Z^{\ast}$ -theorem      30 31 36 38 43 48 79 122 135
Theorems, Glauberman ZJ-theorem      26 38
Theorems, global C(G, S)-theorem      38 53
Theorems, Goldschmidt strongly closed abelian 2-subgroup theorem      43 89
Theorems, Gorenstein — Harada sectional 2-rank at most 4 theorem      39 42 43
Theorems, Gorenstein — Walter dihedral Sylow 2-subgroup classification      50 74
Theorems, Gorenstein — Walter dihedral Sylow 2-subgroup classification, revision by Bender and Glauberman      50 74
Theorems, Hall — Higman theorem B      26
Theorems, Holt’s Theorem      89
Theorems, Jordan — Holder theorem      12ff.
Theorems, local C(X, T )-theorem      50 96–97 129–131
Theorems, Mason quasithin theorem      37 41
Theorems, odd order theorem      30 31 36 38–39 48 79 104 134 135
Theorems, odd order theorem, revision of      48 74 123
Theorems, p-component uniqueness theorems      30–31 38 53 65 90–92 118
Theorems, Schur — Zassenhaus theorem      24
Theorems, signalizer functor theorems      49 124
Theorems, Solomon maximal 2-component theorem      39
Theorems, theorem $U(\sigma)$       5 86 92 106—108 129 131
Theorems, theorem $U(\sigma)$ , corollary $U(\sigma)$       92

Theorems, theorem $U(\sigma)$ , stages      1—3 98—99
Theorems, theorem $\mathcal{C}_1$       104
Theorems, theorem $\mathcal{C}_1$ , stages 1–4      106–108
Theorems, theorem $\mathcal{C}_2$       104
Theorems, theorem $\mathcal{C}_2$ , stages 1–4      110–113
Theorems, theorem $\mathcal{C}_3$       104
Theorems, theorem $\mathcal{C}_3$ , stages 1–3      113
Theorems, theorem $\mathcal{C}_4$       105
Theorems, theorem $\mathcal{C}_4$ , stages 1–4      114–116
Theorems, theorem $\mathcal{C}_5$       105
Theorems, theorem $\mathcal{C}_5$ , stages 1–4      116–118
Theorems, theorem $\mathcal{C}_6$       106
Theorems, theorem $\mathcal{C}_6$ , stages 1–2      118
Theorems, theorem $\mathcal{C}_7$       106
Theorems, theorem $\mathcal{C}_7$ , stages 1–5      118–121
Theorems, theorem $\mathcal{M}(S)$       5 90 99 129
Theorems, theorem $\mathcal{M}(S)$ , stages 1—3      97—98
Theorems, theorem PS      92
Theorems, theorem SA      89 97
Theorems, theorem SE      89—90
Theorems, theorem SE, stages 1—2      95—96
Theorems, theorem SF      89
Theorems, theorem SZ      88—89
Theorems, theorem TS      92 114
Theorems, theorem U(2)      89 97 106
Theorems, Thompson $A\times B$ -lemma      21
Theorems, Thompson dihedral lemma      134
Theorems, Thompson factorization theorem      26 130
Theorems, Thompson N-group classification theorem      38—40 43
Theorems, Thompson order formula      114 136
Theorems, Thompson replacement theorem      26 130
Theorems, Thompson transfer lemma      55 104 122 128
Theorems, Three subgroup lemma      17
Theorems, Timmesfeld root involution theorem      42—43
Theorems, Tits classification of spherical buildings of rank at least 3      73
Theorems, Walter classification of groups with abelian Sylow 2-subgroups      74
Theorems, Walter classification of groups with abelian Sylow 2-subgroups, revision by Bender      74
Thompson subgroup      26 130
Thompson, J. G.      37 39—40 43 48 49 107—108 130
Tightly embedded subgroup      39 43
Timmesfeld, F. G.      37 39 40
Tits system      see “(B
Tits, J.      10 25 34 137
TRANSFER      29 31 74 107
Triality      10
Twisted group, untwisted group      7
Uniqueness case      5 38 43 53
Uniqueness grid      79 83 84 87—89
Uniqueness subgroups, $\mathcal{LC}_p$ -uniqueness subgroup      94
Uniqueness subgroups, 2-uniqueness subgroup      82 87—89
Uniqueness subgroups, near component 2-local uniqueness subgroup      97
Uniqueness subgroups, p-component preuniqueness subgroup      90—93
Uniqueness subgroups, p-component preuniqueness subgroup of strongly closed type      93
Uniqueness subgroups, p-component preuniqueness subgroup, controlling rank 1 or 2 fusion      91—92
Uniqueness subgroups, p-component preuniqueness subgroup, standard      91—92
Uniqueness subgroups, p-component preuniqueness subgroup, wreathed      93
Uniqueness subgroups, p-uniqueness subgroup, p odd      52—53 82
Uniqueness subgroups, p-uniqueness subgroup, p odd, strong p-uniqueness subgroup      52—53 58 63 68 82—83 92—96 99 106
Uniqueness subgroups, strongly $\mathcal{Z}$ -embedded subgroup      87–89 96
Uniqueness subgroups, strongly embedded subgroup      30–31 75 82 87–89 95–96
Uniqueness subgroups, strongly p-embedded subgroup      31 82 91–92
Uniqueness subgroups, strongly p-embedded subgroup, almost strongly p-embedded subgroup      91–94
Uniqueness subgroups, strongly p-embedded subgroup, almost strongly p-embedded subgroup, almost p-constrained      93
Uniqueness subgroups, strongly p-embedded subgroup, almost strongly p-embedded subgroup, of strongly closed type      93
Uniqueness subgroups, strongly p-embedded subgroup, almost strongly p-embedded subgroup, wreathed      93
Uniqueness subgroups, weakly $\mathcal{Z}$ -embedded subgroup      89
Uniqueness subgroups, {2,p}-uniqueness subgroup      53 98—99
Universal covering group      17
Universal version      33
Walter, J. H.      29 38–39 124 126 127
Ward, H.      49
Weak closure method      43
Weakly $\mathcal{Z}$ -embedded subgroup      see “Uniqueness subgroups”
Weyl group      33
Wide $\mathcal{LC}_p$ -type      116
Wong, W.      35
Wreathed p-component preuniqueness subgroup      93
Y-compatible      71
Yoshida, T.      29
Z(J(P))      26
[K]      90
{2,p}-uniqueness subgroup      98
{p, q}-parabolic type      107

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