Gorenstein D., Lyons R., Solomon R. — Classification of Finite Simple Groups: Groups of Noncharacteristic 2 (Part 1 G) :: Электронная библиотека попечительского совета мехмата МГУ

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Gorenstein D., Lyons R., Solomon R. — Classification of Finite Simple Groups: Groups of Noncharacteristic 2 (Part 1 G)

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Название: Classification of Finite Simple Groups: Groups of Noncharacteristic 2 (Part 1 G)

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: 1996

Количество страниц: 232

Добавлена в каталог: 26.03.2005

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Предметный указатель

-property      5
$\mathcal{K}$ -group      2
$\pi$ -component      18
$\pi$ -layer      18
Alperin — Goldschmidt conjugation family      96
Alperin, J.L.      96 144
Amalgam      162
Amalgam method      161—169
Amalgam method, amalgam hypothesis      164
Amalgam method, associated tree      165
Amalgam method, critical pair      166
Amalgam, completion of      162
Amalgam, completion of morphism of completions      162
Amalgam, defining X-amalgam      163 170—174
Amalgam, morphism of      162
Amalgam, morphism of injective, surjective, isomorphism      162
Amalgam, universal completion of      162
Amalgam, X-amalgam      162
Aschbacher x-block      159
Aschbacher, M.      37 79 118 144 150 155 158—159 170
Baer, R.      90
balance      see “Group” (see also “Signalizer functor”)
Balance in solvable groups      16
Balance, $L_{p'}$ -balance, $L*_{p'}$ , -balance      29—31
Balance, $O_{p*}$ -balance      26
Balance, k-balance      118—129
Balance, solvable $L_{p'}$ -balance      82
Baumann, B.      158
Bender method      110—117
Bender, H.      7 16 23 101 110—116 129—130 193 199
Block      195
Block, principal block      195
BN-pair      174—180
BN-pair, rank of      174
BN-pair, saturated      174
BN-pair, split      174
Brauer correspondence      195
Brauer, R.      89 192 193 195—197 198 200—202
Building      174
Burnside, W.      72 97 146 156 199
CHARACTER      188
Character, coherence      193—194
Character, F-character      188
Character, induction      191
Character, inertia group of      191
Character, irreducible      188
Character, isometry of      194
Character, virtual      188
Clifford, A.H.      55 191
Cohomology of groups      58—61
Cohomology of groups, and extensions      60
Cohomology of groups, cochains, coboundaries, cocycles      59
Commutators      3 7 18
Component      6—16 44—53
Component, homogeneous or Wedderburn      54
Component, semirigid      45
Component, standard      107
Component, terminal      34 106
Connected partially ordered set      162
Coprime action      17—18 72—78
Coset complex      see “Simplicial complex”
Coset geometry      163
Coset geometry, critical pair      166
Coset geometry, distance between vertices in      178
Coset geometry, path in      165
Coset geometry, path in interior of      178
Coset geometry, path in length of      178
Cover      2
Covering group      6
Covering group, universal covering group      6
Critical section      12 72—73
Critical subgroup      73
Defect group      195
Delgado, A.      168
Diagonal      13
Diagonal pumpup      31 36
Extensions and cohomology      59—60
Extensions of extra-special 2-groups      183—187
Extensions, split      60
Extremal conjugate      92
Failure of factorization      147—157
Failure of factorization, -module      151
Failure of factorization, failure of factorization module or F-module      148
Feit, W.      1 17 110 133 194
Fitting subgroup      6
Fitting subgroup, generalized Fitting subgroup      6—13 27
Fitting, H.      6
Four-group      3
Frattini argument      18
Frattini Q-conjugacy class      181
Frattini Q-conjugacy class, relative      181
Frattini Q-separated      181
Frattini subgroup      10
Frattini, G.      10 18
Frobenius group      55—56
Frobenius group, Frobenius complement      56
Frobenius group, Frobenius kernel      56
Frobenius, G.      56 98 191
Fusion of p-elements      89 96—100
Fusion of p-elements, by conjugation family      96
Fusion of p-elements, control of      91
Fusion of p-elements, extremal conjugates      92—93
Fusion of p-elements, fusion pattern      89
Fusion of p-elements, isolated p-element      90
Fusion of p-elements, strong fusion pattern      89
Gaschutz, W.      61
Generalized Fitting subgroup      see “Fitting subgroup”
Generation      15—16 74 77—78
Gilman, R.H.      37—38
Glauberman property      5
Glauberman, G.      4—5 23 89 98 100 118 122 140—141 147 149 158 193 196
Goldschmidt, D.      77 85 96 118 122 164
Goldschmidt-O’Nan pair      85 (see also “Module shape of”)
Gomi, K.      168
Gorenstein, D.      5 7 16 118 122
Graph      4 66 126—129 165 176
Green, J.A.      196
Griess pair      184
Griess pair, admissible      185
Griess pair, equivalent      184
Griess type      184
Griess, R.L.      6 184
Group order formulas      198—202
Group with a split BN-pair      174—180
Group with a split BN-pair, root subgroup of      175
Group with a split BN-pair, Weyl group of      174
Group, $(k + \frac12$ -balanced      118
Group, $\pi$ -quasisimple, $\pi$ -semisimple      18
Group, covering      6
Group, covering, universal covering      6
Group, dihedral      2 102
Group, indecomposable      12
Group, k-balanced      118
Group, k-connected      66
Group, locally k-balanced      119
Group, of $\mathcal{L}\mathcal{C}_p$ -type      135
Group, of Griess type      184
Group, of Griess type, full extension of      185
Group, one-headed      8
Group, outer generated      108
Group, outer locally balanced      121
Group, outer p-cyclic      5
Group, p- closed      2
Group, p-constrained      78—79
Group, p-solvable      79
Group, p-stable      141
Group, perfect      2
Group, quasisimple      6
Group, S-quasisimple      22
Group, S-semisimpIe      22

Group, semisimple      6
Group, solvably p-quasisimple      80
Group, solvably p-semisimple      80
Group, strongly locally 1-balanced      130
Group, weakly k-balanced      118
Group, weakly locally fc-balanced      119
Half central      67
Half p-central      67
Hall, P.      7 53 57—58 62 64 73 77 95
Higman, G.      7 53 57—58 73 144
Huppert, B.      94
Hyperplane      3
Involutions      102—103 198—202
Isolated p-element      90
Ito, N.      79
Klinger — Mason method      135—140
Klinger, K.      135
Konvisser, M.      66
Layer      6 12—16
Maschke, H.      55
Mason, G.      135
McBride property      5
McBride, P.P.      5 118 123
Module      53—59
Module, absolutely irreducible      54
Module, completely reducible      54
Module, failure of factorization      148
Module, faithful      54
Module, free      54
Module, Goldschmidt-O’Nan      85—89
Module, homogeneous      54
Module, irreducible      54
Module, quadratic      140
Near component      157—161
Near component, alternating      159
Near component, associated module of      158
Near component, linear      159
Niles, R.      158
Normal p-complement      97
O’Nan, M.      13 85—86
p'-component      19
p*-group      23—28
p-component      16—44
p-component preuniqueness subgroup      106
p-component, $\mathcal{I}_p^0$ -rigid      37
p-component, $\mathcal{I}_p^0$ -terminal      36—43
p-component, (x, K)-bouquet of      41
p-component, (x, K)-bouquet of, height of      41
p-component, Gilman-maximal      38
p-component, p-terminal      43
p-component, solvable      80—85
p-component, strongly $\mathcal{I}_p^0$ -rigid      37
p-core, k-generated p-core      101
p-core, weak k-generated p-core      125—126
p-groups      61—71
p-groups, extra-special      62—64 183—187
p-groups, extra-special, width of      63
p-groups, of maximal class      68
p-groups, of symplectic type      62—64 136—138
p-groups, regular      65
p-groups, regularly generated      181
p-groups, special      62
p-layer      19—21
p-layer, extended p-layer      82
p-layer, solvable p-layer      82
p-part of x      196
p-reducible core      147
p-singular element      201
p-stability      141
Permutation group      3
Permutation group, regular      3
Permutation group, semiregular      3
Peterfalvi, T.      102
Properties of quasisimple groups,       5
Properties of quasisimple groups, local k-balance      119
Properties of quasisimple groups, p-Glauberman      5
Properties of quasisimple groups, p-McBride      5
Properties of quasisimple groups, Schreier, p-Schreier      5
Properties of quasisimple groups, semirigidity      45
Properties of quasisimple groups, signalizer      114—115
Properties of quasisimple groups, stable 2-center      48
Properties of quasisimple groups, stable involution      48
Properties of quasisimple groups, strong local 1-balance      130
Properties of quasisimple groups, weak local k-balance      119
Pumpup      31 36
Pumpup, diagonal      31 36
Pumpup, level unbalancing      122
Pumpup, long      36
Pumpup, nonlevel unbalancing      122
Pumpup, nontrivial      31 36
Pumpup, pumpup-closed set      43
Pumpup, trivial      31 36
Pumpup, unbalancing      122
Pumpup, vertical      31 36
Quadratic action      140
Quadratic action, p-stability      141
Quadratic action, quadratic four-groups      144—146
Quasisimple group      6
Quasisimple group of type S      43
Quaternion group      62
Rank of BN-pair      174
Rank of p-group      3
Rank, 2-local p-rank      52 135
Regular generation      181
Representations of groups      53—59 (see also “Modules”)
S-component      22
S-layer      22
Schreier property      5
Schreier property, p-Schreier property      5
Schreier, O.      5
Schur multiplier      6 186
Schur, I.      6 17 54
Section      2
Segev, Y.      170
Signalizer functors      122—129
Signalizer functors, associated $(k +\frac12$ -balanced functor      124
Signalizer functors, closed      122
Signalizer functors, complete      122
Signalizer functors, k-balanced      124
Signalizer functors, method      118—129
Signalizer functors, nonsolvable      122
Signalizer functors, solvable      122
Signalizer functors, trivial      122
Signalizer functors, weakly k-balanced      124
Signalizers, p-signalizers      110—134
Simplicial complex      164 170—174
Simplicial complex, coset complex      164 170
Simplicial complex, covering of complexes      170
Simplicial complex, simply connected      170
Solomon, R.      37
Stabilizer of a chain      73
Stable 2-center property      48
Stable involution property      48
Steinberg, R.      6 146
Stellmacher, B.      153 158
Stroth, G.      142
Subgroup, focal      90
Subgroup, generalized Fitting      6—13 27
Subgroup, Hall      77
Subgroup, L-preuniqueness      106
Subgroup, linked      111
Subgroup, maximal      110—117
Subgroup, of parabolic type      134—169
Subgroup, offending      148 151
Subgroup, p-local      3
Subgroup, Prattini      10—11
Subgroup, semisimple      6—16
Subgroup, strongly closed      100
Subgroup, strongly embedded      101 103—104
Subgroup, strongly p-embedded      101 104—105

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