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Hinton H. — An introduction to the theory of groups of finite order
Hinton H. — An introduction to the theory of groups of finite order

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Название: An introduction to the theory of groups of finite order

Автор: Hinton H.

Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1908

Количество страниц: 236

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_m$, c, $c_m$ (point-groups)      113 114 212
$\Gamma_m$ (point-group)      114
Abelian group      51
Absolute invariant      99
Abstract group      55
Adjoined groups      167
Alternating group      79
Appendix      233
Automorphism      136
Automorphisms, group of      137
Bauer’s theorem      145
Bilinear form      16
Birational substitution      12
Burnside’s Theorem      186
Canonical Hermitian form      20
Cayley’s colour-groups      86
Central      63 167
Centre of symmetry      42
Characteristic equation      21
Characteristic equation, of a conjugate set      179
Characteristic equation, series      165
Characteristic equation, subgroup      139
Chief-composition-series      164
Chief-factor-groups      164
Chief-factors      164
Chief-series      164
Circular permutation      7
Class of a group      167
Class of a group, of integral functions      28
Class of a group, of outer automorphisms      137
Cogredient automorphism      136
Cogredient automorphism, groups      167
Collinear transformation      44
Collineation      45
Colour-groups      86
Commutant      133
Commutative elements      1
Commutative elements, group      51
Commutator      4
Commutator, of a group      133
Commutator, subgroup      133
Complete group      137
Completely reducible group      100
Component groups      69
Composite group      63
Composition-factor-groups      158
Composition-factors      158
Composition-series      158
Conformal groups      55
Congruent figures      39
Conjugate complex quantities of a Field      32
Conjugate complex quantities of a Field, elements and subgroups      61
Conjugate complex quantities of a Field, substitution      16
Contragredient automorphism      136
CYCLE      8
Cyclic or cyclical group      60
D, $D_m$, $d_m$, $\delta_m$, $\Delta$, $\Delta_m$ (point-groups)      113 114 115
Decomposable groups      67
Definite Hermitian form      20
Degree of a cycle      8
Degree of a permutation      6
Degree of a permutation-group      79
Degree of a substitution      12
Degree of a substitution-group      98
Derived groups      166
Determinant of a substitution      16
Dicyclic group      150 170
Dihedral group      113 170
Direct product      69
Distinct representations      179
E, H (point-groups)      113 115
Element      1
Elliptic substitution      27
Enantiomorphous figures      39
Equivalent representations      179
Equivalent representations, system of points, lines, $\& c$      109
Euler’s construction      36
Even permutation      11
Extended point-groups      114
Factor-group      72
Finite group      51
First adjoined group      135
First adjoined group, central      167
First adjoined group, cogredient      135
First adjoined group, derived group      133
Fractional linear substitution      26
Fractional linear substitution-group      98 107
Frobenius’ theorem      75 156
Galois field      29
Gauss’ Theorem      187
General homogeneous linear substitution-group      105
Generator      55
Generators of an Abelian group      126
Geometrical movement      33
Geometrical movement, representation of a movement      40
Gliding-reflexion      38
Gnomonic projection      47
Greatest commonsubgroup(G.C.S.)      66
Group      51
Group of automorphisms      137
Group of cogredient isomorphisms      135
Group of inner automorphisms      135
Group of isomorphisms      137
Group of movements      108
Hamiltonian group      175
Hermitian form      18
Hermitian form, group      104
Hermitian form, invariant      102
Hermitian form, substitution      16
Hints for solution of the examples      189
Holoaxial point-group      111
Holohedral isomorphism      71
Holomorph      139
Homogeneous linear substitution      12 15
Homogeneous linear substitution, linear substitution-group      98
Hyperbolic substitution      27
Hypohermitian form      20
Icosahedral group, E      113
Identical element      1
Identical element, group      57
Imprimitive group      93
Imprimitive group, systems      93
Independent elements      55
Index of a subgroup      58
Infinite group      51
Inner automorphism      136
Integral mark      29
Intransitive group      79
Invariant element      62
Invariant element, of a substitution-group      99
Invariant element, of an Abelian group      127 130
Invariant element, subgroup      63
Inverse conjugate sets      61
Inverse conjugate sets, element      1
Inverse conjugate sets, representations      179
Inversion about a point      33
Irreducible group      100
Isomorphism      70
Isomorphisms, group of      137
Latin square      82
Lattice      117
Loxodromic substitution      27
Marks of a Galois Field      29
Maximum normal subgroup      158
Merohedral isomorphism      71
Metabelian group      135
Metacyclic group      171
Minimum normal subgroup      162
Modular group      102
Monomial substitution      23
Movement, geometrical      33
Movement, geometrical, of the first or second sort      39
Multiple isomorphism      71
Multiplication      23
Multiplication, table of a group      51
Multiply transitive group      79
n-al rotation or rotatory-inversion      110
Negative permutation      11
Net      115
Non-perspective collineation of order two      47
Normal element      62
Normal element, form of a substitution      26
Normal element, subgroup      63
Normaliser of an element      64
Normaliser of an element, of a subgroup      65
Not-square of a Field      32
O, $\Omega$ (point-groups)      113 115
Octahedral group, O      113
Odd permutation      11
Operation      1
Order of a group      51
Order of an element      2
Order of an element relative to a group      51
Orthogonal substitution      16
Outer automorphism      136
Parabolic substitution      27
Partition      58
Perfect group      133
Period of a mark      31
Permutable elements      1
Permutable elements, element and group      61
Permutable elements, groups      67
Permutable elements, movements      33
Permutation      6
Permutation-group      79
Perspective collineation      47
Point-group      108
Pole of a fractional linear substitution      27
Pole of a homogeneous linear substitution      20
Positive Hermitian form      20
Positive Hermitian form, permutation      11
Prime-power Abelian group      130
Prime-power group      142
Primitive group      93
Primitive group, root of congruence      156 169
Primitive group, root of equation in a Field      31
Primitive group, root of Field      32
Product of elements      1
Product of movements      39
Product of permutations      6
Product of substitutions      12 13
Projective transformation      44
Pseudo-substitution      121
Quadratic group      113
Quaternion group      175
Quotient-group      72
Rank of hypohermitian form      20
Real substitution      16
Reciprocal subgroups      183
Reducible group      100
Reflexions, product of two      33
Regular permutation      8
Regular permutation-group      79
Relative invariant      99
Relative invariant, order      51
Representations      179
Residue of a function      28
Resultant of elements      1
Resultant of two reflexions      33
Rodrigue’s construction      36
Rotation-axis      42
Rotatory-inversion      37 41
Rotatory-reflexion      37
Screw      38
Self-conjugate element      62
Self-conjugate element, subgroup      63
Self-inverse conjugate sets      61
Self-inverse conjugate sets, representation      179
Semi-group      51
Series of adjoined groups      167
Series of derived groups      166
Set of characteristics      181
Similar movements      41
Similar movements, permutations      8
Similarity-substitution      23
Simple group      63 107
Simple group, isomorphism      71
Simply transitive group      79
Soluble group      161
Solutions of examples      189
Speciality of a group      167
Square of a Field      32
Stereographic projection      43
Subgroup      57
Substitution      6 12
Substitution-group      98
Sylow subgroup      153
Sylow’s Theorem      152
Symmetric group      79
Symmetric group, substitution      16
Symmetry      42
Symmetry-axis      42
Symmetry-plane      42
T, $\Theta$, $\theta$ (point-groups)      113 114
Tetrahedral group, T      113
Transform of a group      61
Transform of a movement      41
Transform of a permutation      9
Transform of a substitution      14
Transform of an element      3
Transitive permutation-group      79
Transitive permutation-group, sets      91
Translation      33
Translation-group      110
Transposed substitution      16
Transposition      7
Type of an Abelian group      127 130
Type of any group      167
Unitary substitution      16
Vierergruppe      113
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