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Blichfeldt H.F. — Finite collineation groups: With an introduction to the theory of groups of operators and substitution groups
Blichfeldt H.F. — Finite collineation groups: With an introduction to the theory of groups of operators and substitution groups



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Название: Finite collineation groups: With an introduction to the theory of groups of operators and substitution groups

Автор: Blichfeldt H.F.

Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1917

Количество страниц: 210

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian groups      26 43—45
Abstract groups      30 note
Algebraic integer      188
Alternating groups      54 60—61
Associative law      5 30
Bagnera, G.      147 175 176
Bieberbach, L.      97 103 176
Binary groups      63—75
Blichfeldt, H. F.      29 80 102 103 115 116 147 175 176
Boulanger, A.      182
Burnside, W.      4 29 60 80 113 116 123 135 137 138 176
Canonical form      3 24—27
Change of variables      15—17
Characteristic equation      27—28
Characteristics      28 117
Characteristics, general theory      116—138
Characteristics, of inverse and conjugate transformations, and of substitutions      118
Cole, F. N.      29 60
Collineations and collineation groups      10—12
Commutative law      5 31
Components of an intransitive linear group      117
Composition of two groups      125
Congruences      183—84
Conjugate operators, sets, and subgroups      36—38
Conjugate-imaginary groups      18
Cycle of a substitution      52
Cyclotomic number      179
Degree of a substitution group      is the number of distinct letters used in the substitutions of the group
Demoivre, A.      187
Determinant of a linear transformation      2 13 exsercise 4
Dickson, L. E.      29 30 61 116 176 177
Differential equations having algebraic solutions      180—82
Dihedral group      70
Diophantine equation      75
Domain      177 180
Equation of the fifth degree      179—80
Equivalent groups      64 129 135
Even substitutions      53
Factor groups      42—43
Finite groups      33
Form problem      179
Frobenius, G.      4 97 102 103 116 119 124 176
Fuchs, L.      21 65 174
Galois, E.      177
Galoisian resolvent      177
Galois’ theory of equations, with Klein’s extension      177—80
Generators      9—10 33 39 exsercise 139
Gordan, P.      65 175
Goursat, E.      165 175
Group characteristics      116—38
Group of an equation      178
Group of similarity-transformations      13 exsercise
Group-matrix      133—35
Groups of linear transformations      7—15
Groups of operators      33 117
Groups of order $p^a$      45—50 80 81
Groups of order $p^aq^b$      137
Groups of substitutions      54 56—59
Groups of the regular polyhedra      69—73
Groups, leaving invariant a quadric surface      169 exsercise 2
Hermite, C.      19
Hermitian form      19
Hermitian invariant      20—21
Hessian group      109
Hilton, H.      29
Holder, O.      60
Huntington, E. V.      30
Icosahedral group      73
Identity, the      3 30 51 9 33
Imprimitive linear groups      76—79
Imprimitive substitution groups      55
Index of a subgroup      34
Intransitive linear groups      17
Intransitive substitution groups      55
Invariant operators and subgroups      39—40
Invariants      120 125
Inverse of a linear transformation      5 7 exsercise 5 6 9 22
Inverse of a substitution      51
Inverse of an operator      31 32 exsercise 33
Irreducible algebraic equations      177
Irreducible differential equations      180
Irreducible groups      22—24
Isomorphism      40—43 117
Jordan, C.      4 60 64 65 73 103 109 115 142 174 175 176 182
Klein, F.      4 65 142 170 174 175 176 178 180 182
Kronecker, L.      124 186 187
Linear fractional groups      13
Linear groups      8
Linear transformations      1—7
Ling, G. H.      60
Loewy, A.      21
Manning, W. A.      177
Maschke, H.      112 135 141 142 159 163 170 176
Matrices of the transformations of a transitive linear group      135 exsercise 2 176 177
Matrices of the transformations, sum and product of      4 119
Matrix of a linear transformation      2
Miller, G. A.      29 60 113
Mitchell, H. H.      115 175 176
Molien, T.      116 176
Monodromie group      182
Monomial groups      77 80
Moore, E. H.      21 61 141 159 161
Multiplication-table of a group      40
Multipliers of a linear transformation      3 7 exsercise 102 exsercise 2
Netto, E.      29
Non-equivalent groups      64 135
Octahedral group      72
Odd substitutions      53
Operators      1 30
Order of a group of operators      33
Order of a linear group      8 82 127 129 exsercise
Order of a linear transformation      6
Order of a primitive linear group      39 92 103
Order of a subgroup      34
Order of an operator      32 35
Painleve, P.      182
permutations      50
Picard, E.      21
Power of a linear transformation      5
Power of an operator      32
Primitive linear groups      77 94 96 101 103
Primitive substitution groups      55
Product of linear transformations      3—5
Product of matrices      119
Product of operators      30
Product of substitutions      51
Quaternary groups      139—73
Quotient groups      42—43
Reduced set      23
Reducible groups      22—24
Regular substitution group      59 131 135
Roots of unity      186
Schur, I.      4 103 116 119 129 176 177
Schwarz, H.      174
Schwarzian derivative      182
Self-conjugate operators and subgroups      39—40
Set of generators      33
Set of non-equivalent component groups      131
Sets of conjugate operators      36
Sets of conjugate subgroups      38
Sets of imprimitivity (of a linear group)      77
Sets of intransitivity (of a linear group)      18
Sets of intransitivity (of a substitution group)      55
Similarity-transformations      3 7 exsercise 13 exsercise 18 exsercise 40 exsercise
Simple groups      39 58 60—61 137 138 exercise 147
Subgroups      8 34—35 46 49 exsercise
Substitutions      50
Substitutions, written as linear transformations      1 118
Sum of matrices      119
Sylow, L.      46
Sylow’s theorem and Sylow subgroups      46—50 80 147
Symmetric group      54
Systems of imprimitivity (of a substitution group)      55 (see also “Sets”)
Ternary groups      104—15
Tetrahedral group      71
Transform of an operator is the operator into which the given operator is transformed      36
Transformations      see “Linear transformations”
Transitive linear groups      17 131
Transitive substitution groups      55
Transposition      53
types of groups      140
Unit circle      94
Unitary form      21—22 24 27
Valentiner group is the group (I)      113
Valentiner, H.      21 65 73 97 115 175 176 180
Variety of a linear transformation and of an abelian group      90
Weber, H.      4
Wiman, A.      180
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