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