Griess R.L.Jr. — Twelve sporadic groups :: Электронная библиотека попечительского совета мехмата МГУ

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Griess R.L.Jr. — Twelve sporadic groups

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Название: Twelve sporadic groups

Автор: Griess R.L.Jr.

Аннотация:

The finite simple groups come in several infinite families (alternating groups and the groups of Lie type) plus 26 sporadic groups. The sporadic groups, discovered between 1861 and 1975, exist because of special combinatorial or arithmetic circumstances. A single theme does not capture them all. Nevertheless, certain themes dominate. The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. A leisurely and rigorous study of two of their three generations is the purpose of this book. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 172

Добавлена в каталог: 22.12.2013

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Предметный указатель

Hamming weight      25
Happy Family      1 131
Harada, Koichiro      134
Held, Dieter      134
Heptacode [4,2,3]      29 122
Hermitian inner product      26
Hexacode balance      34
Hexacode, $\mathcal{H}$       2 30ff
Hexad      80
HI-representation      10
Higman — Sims group      104 116
Higman — Sims group on 100 and 176 points      114
Higman, Donald      116 123
Higman, Graham      134 136
HiS      104 116
HJ      104 123
Holomorph      20
Holt      13
Homological algebra      1
Huppert      20
Indecomposable root system      23
Interpreter, left and right      84
Involutions acting on $\mathcal{G}$       109
Involvement table      153
Isometric      21
Isotropic      25 92
Isotropic subspaces, formula for the number of      28
j, elliptic modular function      135
Janko, Zvonimir      135 137
Jordan canonical form      85 107
Jordan's Theorem      3
k-fold transitivity      5
Kernel of extension      11
L      see "Lattice"
L( $\mathcal{T}$ )      55ff
L( $\Xi$ )      55ff
Labeled set      77
Labeled set, associated      78
Labeling analysis for a frame      102
Labeling map, 6-tuple      39
Labeling map, i-th component      39
Labeling Procedure      44 82ff
Lattice      1 88
Lattice; determinant; volume; automorphism group of a lattice; signature of a lattice; positive definite lattice; negative definite lattice; indefinite lattice; hyperbolic lattice; dual of a lattice; L*      89
Lattice; integral lattice; ambient vector space (for a lattice); nondegenerate, radical      88
Leech lattice      1 86 95ff
Leech triangle      37
Left interpreter      85
Leon, Jeffrey      134
Liber product      132
Lie type, finite groups of      16
Linear error correcting codes      24 25
lines      10
Long Exact Sequence      12
Ly      136
Lyons, Richard      136 137 138
M      95
Maps(A,B)      9
Mathieu groups      1
Maximal subgroups of $M_{24}$       54
Maximal subgroups of Aut( $\Lambda$ )      127
Maximality of $N_{24}$       100
McKay, John      134 135 136
MCl      104 108
McLaughlin group      104 108
Meierfrankenfeld, Ulrich      133
Minimum weight      25
Modular forms      92
Mon(12,3)      85
Mon(n,F), Mon*(n,F)      26 27
Monomial matrices      9 85
Monomial transformation      26
Monster      1 13
Monster type      133
Monster, Baby      134
Moonshine      134
Moufang loop      133
Multiplication by $\omega$       42 43
Multiplier, Multiplikator      15
Natural bilinear form      25
Natural quadratic form      25
Natural transformations      12
Niemeier lattice      93
Niemeier lattice without roots      96
Niemeier lattice, theta function of      96
Nondefective      24
Nondegenerate      21
Nonsingular      24
Nonsplit      11
Normalizer of a subgroup of order 11      106
Norton, Simon      3 132 134
O'Nan, Michael      137
Octad      36
Octad triangle      37
Orbit decomposition      54
Orbits of Aut( $\mathcal{TG}$ ) on $\mathcal{TG}$       87
Orbits of ZS on $\mathcal{H}$       31
Order      10
Orthogonal group      21
Overweight $A^{24}_{1}$ -lattice      98
p-group      19
p-local subgroup      104
Parameters for a code      25 39
Parameters for rank 3 groups: n, k, l, $\lambda$ , $\mu$ , $\lambda_{1}$ , $\mu_{1}$ , d, $f_{i}$       124
Pariahs      2 131 135
Parity      40
Parker, Richard      3 137
Partial holomorph      20
Partition      9
Patterson, N.J.      127
Pentacode, [6,3,4]      29 122
Perfect 1-error correcting code      35
Perfect field      20
Perm(6,4)      30
Perm(n,F)      26
Permutation group      5ff
Permutation module      6
Permutations, useful      49
PGL(2,11)      56 63 66
POINTS      10
Polynomial identity      133
Presentation of symmetric and alternating group      22
Presentation, Chevalley — Steinberg      22
Primitive permutation group      5
Projective involutions      112
Projective plane      10
PSL(2,1)      14 56 61
PSL(2,11)      64 66
PSL(2,23)      56 66
PSL(2,7) labeling      73
PSL(2,9)      18
PSU(3,5)      108 114
PSU(4,3)      108
PSU(6,2)      123
Pullback      132
Pure subspace      69
Quadratic form; bilinear function associated to a quadratic form; defective; degenerate; nondegenerate; nondefective; nonsingular; singular; totally singular      24
Quartet      81
Quartet, standard      81

Quotient of extension      11
R( $\mathcal{O}$ )      54ff 109ff
R( $\mathcal{T}$ )      54ff
R( $\Xi$ )      54ff
R(i)      59
Rank 3      116 123ff
Representation group      15
Right interpreter      84
Robinson, Derek      19
Romans, I, II, III      67
Root group      9 68
Root system      23 93ff
Roots      93ff
Ru      136
Rudvalis, Aranas      136
S=VT      30
Scalar labeling      39
Schur multiplier, Multiplikator      15
Schur — Zassenhaus theorem      8
Segev, Y.      133
Self orthogonal      26 76
Semiintegers $\frac{1}{2}+\mathbf{Z}$       95
Semilinear map      68
Semisimple elements in orthogonal groups      117
Septacode, [4,2,3]      29
Sextet      38
Sextet labelings, useful      48
Sextet stabilizer      42
Sextet, unordered      41
Sharp transitivity      5 85
Short exact sequence      11
Shuffle labeling      84
Shult, Ernest      35
Signed point      77
Simplicity of $Aut(\mathcal{J})/<-1>$       84
Simplicity of .223      107
Simplicity of HiS      114
Simplicity of PSL(m,q)      75
Sims, Charles      116 136 137
Simultaneous componentwise downward extension      22
Simultaneous componentwise upward extension      22
SL(2,3)      29
Sl(n, q)      18 19
slope      67
Smith, Peter      134
Smith, Steve      133
SO(n,K)      23
Solomon, Ronald      137
Solvable doubly transitive group on 9 points      87
Sp(2n,q)      18 19
Sp(6,2)      123
Special 6-set      69
Special hexad      80
Spectra of the $\vartheta_{k}$       118
Spectrum      116
Spin(n,K)      23
Split extension      11
Sporadic simple groups      1 17 131
Square lattice      91
Stabilizer      5
stabilizers      125 126
Standard basis      26 48 84 95
Standard frame in Leech lattice      95 98
Standard Leech lattice      95
Standard quartet      81
Steinberg group      22 23
Steinberg, Robert      15
Steiner system      36
Steiner system $\mathcal{S}$ (5,6,12)      80
SU(4,2)      118
Supp      79
Suz      104 120 124 127ff
Suzuki group      104 120 124 127ff
Suzuki rank 3 sequence      124
Sylow 11-normalizers      63
Sylow 23-normalizer      99
Symbols for sporadic groups      4
Symmetric and alternating group      7
Symmetric and alternating group presentation      22
Symmetric difference      24
Symmetric relation      124
System of imprimitivity      5
Ternary Golay code      2 78 83 102
Ternary Golay code, uniqueness      83
Tetracode, $\mathcal{T}$       76
Tetracode, error correcting properties of      77
Thackray, Jonathan      3 137
Theta function of $E_{8}$ , $HS_{16}$       92
Theta function of Niemeier lattice      96
Theta function or theta series      92 113
Thickened codes      27
Thickened extended Hamming code      72
Thompson's transfer theorem      8
Thompson, John      8 134 135
Tits, Jacques      132 133
Todd, John      36 54
Totally singular      24
Transitivity      5
Transitivity of $M_{24}$ on dodecads      61
Transitivity of $M_{24}$ on octads      57
Transitivity on frames      99
Transitivity on triangles of type 233      113
Transitivity on type 2 vectors      98
Transitivity on type 3 vectors      101
Transposition group, {3,4}-      128 133
Transverse 6-set      69
Triangle of type abc      101
Triangular group      9
Trio of octads      54 121
Type n      95
Uniqueness of Golay code      46
Uniqueness of the Monster      133
Uniserial module      53
Universal group of type $\Phi$       23
Universe      69
Unordered sextet      41
UP1, UP18, UP19      73
UP1, UP2, ...      49ff
UP9      86
Useful permutations      49ff
Useful sextet labelings      48
Venkov, B.B.      93
Weakly closed      104 112
Weakly self orthogonal      26
Weight distribution      38 80
Well balanced sets, $\mathcal{W}$       40
Weyl groups      91 92
Wilson, Robert      127
Witt index      21 122 131
Witt, Ernst      19 115
x', x''      102
[12,6,w]-ternary code      80 83
[24,12,8]      27
[24,12,w]      38
[4,2,3]      27 29
[6,3,4]      29
[7,3,4]      27
[8,4,4]      27
[ijkl]      119
{3,4}-transposition group      128 133

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