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Yale P.B. — Geometry and Symmetry
Yale P.B. — Geometry and Symmetry

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Название: Geometry and Symmetry

Автор: Yale P.B.

Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 288

Добавлена в каталог: 23.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      4
Affine form of a linear transformation      181
Affine space      159
Affine subspace      161
Affine transformation      175
Aleksandrov, A. D.      199
Algebraic element over a field      121
Allendoerfer, Carl B.      83
Alternating 2q-prism      97
Alternating group of degree n      23
Annihilator      254
Anti-representation      23
Artin, Emil      83 210 278
Associative product      4
Automorphism of a field      187
Automorphism of a group      24
Axis of a half-turn      52
Axis of a perspectivity      224
Axis of a rotation      57
Axis of a screw displacement      58
Bachmann, Friedrich      83
Baer, Reinhold      278
Basic parallelepiped      101
Basis of a vector space      126
Beaumont, R. A.      83
Beckenbach, Edwin F.      43
Bilinear forms      260
Birkhoff, Garrett      43 118 157 199
Body-centered lattice      113
Bounded set in an affine space      191
Bounded set in euclidean space      86
box      189
Brauer, Richard      278
Bravais lattice      113
Buckley, J. T.      199
Burckhardt, J. J.      118
Burnside, William      37 43
Canonical basis      129
Cardinality of a set      2
Cassels, J. W. S.      118
Cauchy sequence      88
Cayley representation theorem      22
Cayley-Hamilton theorem      153
Center of a dilatation      68
Center of a group      28
Center of a pencil of lines      212
Center of a perspectivity between lines      212
Center of a perspectivity of space      228
Center of an inversion      52
Central collineation      225
Central dilatation, affine      172
Central dilatation, euclidean      68
centralizer      36
Characteristic of an affine space      176
Characteristic of an affine space, of a field      122
Characteristic of an affine space, polynomial      149
Characteristic of an affine space, subset of a group      28
Characteristic of an affine space, subspace      149
Characteristic of an affine space, value      149
Characteristic of an affine space, vector      149
Choice principle      39
Class equation      33
Codomain      2
Collineation, affine      184
Collineation, euclidean      52
Collineation, projective      226
Commutative diagram      142
Commutative product      4
Commutator      28
Complementary subspaces, affine      177
Complementary subspaces, projective      241
Complementary subspaces, vector      128
Complete group      27
conic      262
Conjugacy class in a group      13
Conjugate points in a polarity      269
Conjugate subgroups      15
Contraction mapping, affine      197
Contraction mapping, general      50
Convex set      188
Coordinate mapping, affine      170
Coordinate mapping, projective      215
Coordinate mapping, vector      138
Correlation      258
Countable set      87
Coxeter, H. S. M.      43 83 118 199 278
Crystal class      106 114
Crystal system      109
Crystallographic group      114
Crystallographic point group      103
Crystallographic restriction      104
Crystallographic space group      114
Cubic crystal system      112
Cubic lattice      102 103
Curie, P.      91 118
Cycle notation for permutations      10
Cyclic group      5
Danzer, Ludwig      199
De Bruijn, N. G.      43
Degenerate quadric      264
Degree of a representation of a group      21
Degree of a symmetric group      9
Degree of an element algebraic over a field      121
Desargues’ theorem      205—207
Determinant of a lattice      101
Determinant of a matrix      149
Dieudonne, Jean      157 278
Dihedral group      93
Dilatation ratio      174
Dilatation, affine      171
Dilatation, euclidean      68
Dimension of a lattice      99 194
Dimension of a projective space      202 203
Dimension of a vector space      127
Dimension of an affine space      164
Direct similarity      60
Directing space of an affine space      161
Direction of a translation      57
Direction of an affine reflection      178
Discrete group, affine      192
Discrete group, euclidean      87
Displacement      62
Domain      2
Dual basis      253
Dual figures      93
Dual space of a projective space      254
Dual theorems in projective geometry      213
Duality, linear      254
Duality, principle of      212
Duality, projective      255
Ebey, Sherwood      188
Echelon form      129
Eigenvalues      149
Elation      228
Elliptic projectivity      243
Enantiomorphic space groups      115
End-centered lattice      113
Escher, M. C      83
Euclidean group      46
Eulerian angles      84
Exactly transitive      159
Face of a parallelepiped      191
Face-centered lattice      102 113
Faithful representation      20
Fiber group      117
Field      121
Field extension      121
Fixed, globally      11
Fixed, hyper-      227
Fixed, linewise      227
Fixed, pointwise      11
Fomin, S. V.      83
Full symmetric group      9
Function      2
Fundamental domain      101
Fundamental theorem of geometry, affine version      171
Fundamental theorem of geometry, classical projective version      236
Fundamental theorem of geometry, version for collineations      249
Fundamental theorem of geometry, version for projectivities      236
Gardner, Martin      199
General linear group      154
General position in an affine subspace      164
General position with respect to a group of isometries      77
Generators of a projective subspace      209
Generators of a subgroup      5
Generators of a vector subspace      126
Generators of an affine subspace      163
Gleason, A. M.      278
Glide reflection      58
Globally invariant      11
Golomb, S. W.      43
Graph of a homogeneous system in a projective space      221
Graph of a linear system in an affine space      170
Grassmann space      244
Group      4
Group of the cube      12
Group of the square      16
Grunbaum, Branko      199
Guggenheimer, Heinrich      83 118
Half-turn      52
Hall, Marshall      43 278
Halmos, Paul R.      278
Harmonic conjugate      239 241
Harmonic homology      242
Hemihedry      112
Henry, N. F. M.      118
Herstein, I. N.      43 157
Hexagonal crystal system      112
Hilbert, David      118
Hirsch, K. A.      43
Holohedry      109
Homogeneous coordinates      214
Homogeneous equations      220
Homogeneous mappings      48
Homology      228
Homomorphism of a group      18
Homomorphism of a ring      122
Homothetic transformation      68
Hyper-fixed      227
Hyperbolic projectivity      243
Hyperplane at infinity      202
Hyperplane, affine      164
Hyperplane, projective      202
Icosahedral group      93
Identity element in a group      4
Identity function      3
Improper congruence      62
Independent points, affine      164
Independent points, euclidean      46
Independent points, projective      216
Independent vectors      126
Index of a quadric      270
Index of a subgroup      34
Initial vertex of a parallelepiped      189
Inner automorphism      25
Integral basis of a lattice group      193
Integral matrix      195
International Tables of X-Ray Crystallography      116 118
Invariant, globally      11
Invariant, pointwise      11
Invariant, subset of a group      28
Inverse element in a group      4
Inverse function      3
Inversion with center X      52
Involution, affine      176—178
Involution, euclidean      52
Involution, linear      135—137
Involution, projective      238—243
Isometry      46
Isomorphism      20
Isotropic      270
Join of two projective subspaces      209
Join of two subgroups      7
Kernel of a homomorphism      18
Kernel of a linear transformation      132
Killgrove, R.      278
Klee, Victor      199
Kolmogorov, A. M.      83 199
Kurosh, A. G.      43
Lagrange’s Theorem      33
Lang, Serge      199
Latent values      149
Lattice      99 192
Lattice group      99 192
Lattice, body-centered      113
Lattice, body-centered cubic      102 103
Lattice, end-centered      113
Lattice, face-centered      113
Lattice, face-centered cubic      102
Lattice, primitive      112
Lattice, primitive cubic      102
Lavrentev, M. A.      199
Le Corbeiller, Phillipe      118
Length of a translation      57
Levine, Jack      157
Lightstone, A. H.      157
Limit point      87
linear combination      125
Linear functional      253
Linear transformation      132
Linearly dependent      126
Linewise fixed      227
Lomont, J. S.      119
Lonsdale, K.      118
MacGillavry, Caroline H.      83
MacLane, Saunders      43 157 199
Mapping      2
Matrix of a linear transformation      140
Matrix representation      21
Meyer, Jean-Pierre      199 278
midpoint      177
Miller, D. W.      43
Minimal polynomial      121
Mirror of a euclidean reflection      52 Mirror of a perspectivity
Mirror of an affine reflection      178
Mitchell, Barry      157
Modenov, P. S.      83
Monoclinic crystal system      112
Moser, W. O. J.      43
Mostow, George D.      199 278
Motions      62
Nahikian, H. M.      157
Natural basis      126
Natural matrix      139
Net group      117
Nomizu, K.      199
Noncommutative field      275
Nonsingular linear transformation      154
Nonsingular semi-linear mapping      187
Nontrivial permutation      8
Normal subgroup      20
Normal subset      28
normalizer      33 36
Null system      267
Nullity of a linear transformation      221
Octahedral group      93
One-to-one correspondence      2
One-to-one function      2
Onto function      2
Opposite similarity      60
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