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| Авторизация |
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| Opechowski W. — Crystallographic and metacrystallographic groups |
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| Предметный указатель |
Magnetic structure 475
Magnetic structure of  490
Magnetic symmetry 359 475
Magnetic translation group N15.1
Magnetic unit cell 421
Magnetically admissible groups of rotations 480 T18.1
Magnetically admissible point groups 480 T18.1
Magnetically induced magnetoelectric effect N19.3
Magnetically ordered crystal 355 490
Magnetically ordered solid 475 490
Magnetoelectric crystalline medium (linear) 499
Magnetoelectric crystalline medium (non-linear) 498
Magnetoelectric effect 502
Magnetoelectric medium 395
Magnetoelectric point groups 499 T19.1
Main Theorem on Permutation Representations 73 74
Major Shubnikov group 361
Mapping of a set into a set 4 5 8
Mapping of a set onto a set 5
Maschke's Theorem 133
Mass-valued function 353 380
Matrix (square matrix), adjoint of a 76
Matrix (square matrix), augmented 114
Matrix (square matrix), characteristic equation of a 76
Matrix (square matrix), diagonalizable 77
Matrix (square matrix), eigenvalues (= characteristic values) of a 76
Matrix (square matrix), Hermitian 77
Matrix (square matrix), Hermitian adjoint of a 76
Matrix (square matrix), non-singular 15
Matrix (square matrix), orthogonal 76
Matrix (square matrix), symmetric 76
Matrix (square matrix), trace of a 76
Matrix (square matrix), transpose of a 76
Matrix (square matrix), triangular 100
Matrix (square matrix), unimodular 79
Matrix (square matrix), unitary 76
Matrix corepresentation = corepresentation
Matrix group = group of  matrices = \mathbb
Matrix group, adjoint 77
Matrix group, complex conjugate 77
Matrix group, general inhomogeneous linear, $GIL(n) 113
Matrix group, general linear complex,  16 76
Matrix group, general linear integral,  75
Matrix group, general linear rational,  79
Matrix group, general linear real,  16
Matrix group, inhomogeneous orthogonal 116
Matrix group, magnetic linear,  81 419 N2.8b
Matrix group, real orthogonal,  79 109
Matrix group, special inhomogeneous linear,  119
Matrix group, special linear integral,  79
Matrix group, special linear rational,  79
Matrix group, special linear real,  79
Matrix group, special real orthogonal, $SO(n, \mathbb R) = 
Matrix group, special unitary,  11
Matrix group, unitary,  11
Matrix representation of a group 14 131 134
Matrix representations of a finite Abelian group 136
Matrix representations of a finite cyclic group 136
Matrix representations of a finite transitive group of permutations 136
Matrix-algebraic derivation of three-dimensional space groups N7.ll
Maximal axial group of rotations 160
Maximal subgroup 15
Maximal subgroups of  and their subgroups T9.1.1 T9.1.3
Maxwell equations 395 N14.1
Members of a partition of a set 6
Metacrystallographic group 11 310 352 353 360
Metacrystallographic group of Kind (i) 352 353 354
Metacrystallographic group of Kind (ii) 352 354
Metacrystallographic group of Kind (iii) 352 355
Metric form associated with a basis of a point lattice 207
Metric form associated with a basis of a vector space 96
Metric form associated with a coordinate system 98
Metric properties (= metric) of a Euclidean point space 98
Metric properties (= metric) of a Euclidean vector space 96
Metric properties (= metric) of a unitary vector space 521
Metric properties (= metric) of lattice groups 205
Microscopic field equations of Lorentz 398
Minimal set of generators of a subgroup 17
Minkowski space 101
Minor Shubnikov group 361
Mirror line 163
Mirror plane 150
Mirror plane of a rotatory reflection 151
Modulated crystal 537 548 N22.ll
Modulated point lattice, one-dimensional 539
Modulated point lattice, three-dimensional 545
Modulation function 539 545
Modulo equality 7 21
Monoclinic Bravais system of point lattices 244 T8.3
Monoclinic Bravais system of space groups T9.2.2
Monoclinic geometric-class systems of groups of rotations T6.2 T6.5
Monoclinic groups of rotations T6.2 T6.5
Monoclinic ITC-system of space groups T9.2.2
Monoclinic point lattice, primitive 244
Monoclinic point lattice, side centred 244
Monomorphism 23
Motion = rigid motion = isometry 115 N4.4
MP-Heesch group 397 T19.1
Multiple colour group 384
Multiple d-colour group 386
Multiple direct product group 53
Multiple two-colour group 360 386
Multiplication of a vector by a complex number 88
Multiplication of elements of a group 10
Multiplication rule for the elements of a semidirect product group 28
Multiplication table of a group 11
Multiplicative group of complex numbers 51
Multiplicative group of real numbers 51
Multiplicative notation for products of elements of an Abelian group 15
N-fold axis of a group of proper rotations 155
Naive set theory N1.1
Natural coordinate system for a lattice group 202
Natural coordinate system for a point lattice 203
Natural coordinate system for a space group 257
Natural coordinate systems 119
Natural homomorphism 23
Natural matrix representation of a group of permutations 35 36 37
Negative sublattice of a magnetic point lattice 420
Net group 62 196 306 N7.4 Nll.l
Net group as a subgroup of a three-dimensional space group 313
Net group associated with a two-dimensional space group and the inversion group of a line 308
Net group in space 312 T11.2
Net-group family of a two-dimensional space group 310
Net-group superfamily and reduced superfamily of the two-dimensional space group pm T11.3
Net-group superfamily of a two-dimensional space group 310
Neumann's Principle 497 498 N19.1
Newton group 103 165 N6.4 N6.5 N14.1
Newton-group elements of the same kind 168
Non-characteristic crystallographic orbit for a space group N10.4
Non-crystallographic magnetic group of rotations = non-crystallographic magnetic point group 408
Non-exceptional Bravais subclass of space groups 270
Non-exceptional space group 270
Non-primitive translation 259
Non-primitive translation associated with a rotation 259 325
Non-primitive unit cell of a crystal 292
Non-primitive unit cell of a point lattice N8.2
Non-singular square matrix 15
Non-symmorphic line group 325
Non-symmorphic space group 255 274 N9.3
Non-symmorphic space group associated with a symmorphic space group 258
Non-trivial magnetic group 402
Non-trivial spin group 506
Non-trivial spin group corresponding to a magnetic group 509
Non-trivial spin groups compared to colour groups 515 517
Norm (= length) of a ray 522
Norm (= length) of a vector 522
Normal form of a rotation 151
Normal polyhedron 497
Normal subgroup 19 20 21 26 47
Normalizer of a subgroup 25
| Null-vector = zero-vector 88
NWB system of space groups 279
O(n) =  see matrix groups
O-equivalent (= orthogonally equivalent) matrix groups 81
O-subgroup of a space group 260
O-supergroup of a space group 260
Oblique Bravais system of point lattices T8.2
Oblique Bravais system of space groups T9.1.3
Oblique geometric-class system of groups of rotations T6.7
Oblique groups of rotations T6.7
Oblique ITC-system of space groups T9.1.3
Oblique point lattice 234
Octahedral group = cubic group 155 T6.2 T6.5
Odd permutation 34
One-colour group 364
One-dimensional Euclidean point space 164
One-dimensional modulated point lattice 539
One-sided line group 312 330 Tll.1.1
One-sided line strip 312 330 Tll.1.2
One-to-one correspondence between two sets 5
Operator acting on a function space 44 351 530
Operator acting on a set 5 44
Opposite isometry 121 148 162
Opposite orientations 119 120
Opposite symmetry classes of a point set 193
Orbit of a point under action of a group of isometries = point set generated by a group of isometries from a point 189
Orbit of a point under action of a space group = (geometric) simple crystal 290 N10.1
Orbit of an element of a set 38
Order of a class of conjugate subgroups 26
Order of a group 11
Order of an element of a group 17
Ordered basis of a vector space 89
Ordered n-tuple of elements of a set 4
Ordered pair of elements of a set 4
Ordinary space (three-dimensional Euclidean point space) 87 101 148
Orientation classes of bases 119
Orientation classes of coordinate systems 120
Orientation — handedness 119
Orientation-preserving subgroup of a group of affine transformations 121
Orientation-preserving subgroup of a group of linear transformations 121
Orientation-preserving subgroup of an affine group 121
Orientation-preserving subgroup of the linear group 121
Orthogonal basis 97 520
Orthogonal equivalence of matrix groups = O-equivalence 82
Orthogonal group of a vector space 103 108
Orthogonal matrix 76
Orthogonal transformation of a Euclidean vector space 108
Orthogonal vectors 95 519
Orthogonal-matrix group (real) 79 109
Orthogonality relations of the characters of an irreducible matrix representation 146
Orthogonality relations of the matrix elements of an irreducible matrix representation 146
Orthonormal basis 97 521
Orthorhombic Bravais system of point lattices T8.3
Orthorhombic Bravais system of space groups T9.2.2
Orthorhombic geometric-class system of groups of rotations T6.2 T6.5
Orthorhombic groups of rotations T6.2 T6.5
Orthorhombic ITC-system of space groups T9.2.2
Orthorhombic point lattice, base-centred 244
Orthorhombic point lattice, body-centred 244
Orthorhombic point lattice, face-centred 244
Orthorhombic point lattice, primitive 244
Outer automorphism 46
P-Heesch group 39 397 T15.3 T19.1
P-Heesch — Shubnikov group 494
P-symmetry group 360
Parallel lines 93
Parallel point sets 190
Parallel sublattices 204
Paralleletope 210
Parity of a permutation 34
Partition associated with an equivalent relation 7
Partition of a set 6 8
Passive interpretation of a matrix equation 107
Perfect crystal 293
Periodic function defined on a point lattice 538
Periodic group of isometries 196
Permutation matrix 36
Permutation of a group 45
Permutation of a set = transformation of a set onto itself 5 30
Permutation representation as an h-subgroup 75
Permutation representation of a group 24 68
Permutation representation of a group generated by a subgroup 68
Permutation-matrix representation of a group 71
Permutational colour groups 360 N13.5
Phase factor 520
Physical crystal 293
Piezoelectric crystalline medium 497
Plane = two-dimensional Euclidean point space 162
Plane in an affine point space 93
Poincare' group N6.5 N14.1
Point 92
Point complex 328
Point endowed with mass = mass-point 349
Point generated by an isometry from another point 188
Point group = group of rotations 149
Point group of a Bravais space group 219
Point group of a Bravais superspace group 552
Point group of a direct product of a space group and the time group 439
Point group of a geometrical crystalline medium 496
Point group of a group of affine transformations 128
Point group of a Heesch — Shubnikov group 439
Point group of a magnetic space group 439 N17.3
Point group of a magnetic space group M of the kind  439
Point group of a magnetic space group M of the kind  439
Point group of a physical crystalline medium 497
Point group of a space group 250
Point group of an infinite decomposable group of isometries 306
Point lattice 98 195 196 201
Point lattice associated with a positive definite symmetric matrix 208 209
Point set 188
Point set invariant under an isometry 191
Point sets generated by a group of isometries 188
Point sets generated by a line group 327
Point sets generated by a space group = (geometrical) crystal 196
Point sets generated by the group  192 T7.1
Point sets having opposite symmetry 193
Point sets having the same symmetry 193
Point sets in space (one-, two-, and three-dimensional) 190
Point space 92 98
Point symmetry 303
Pointwise-fixed geometrical invariant 153
Polar lattice = reciprocal lattice N8.3
Polar vector 392
Polar vector function 392
Polychromatic group = colour group 354 364
Polyhedral groups 155
Position (= Wyckoff position) for a space group 295
Positive definite symmetric matrix associated with a basis of a vector space 96
Positive definite symmetric quadratic form (= metric form) and the corresponding positive definite symmetric matrix 96 208
Positive definite symmetric quadratic form (= metric form) associated with a basis of a vector space 96 207
Positive sublattice of a magnetic point lattice 420
Power set group N2.1
Power set of a set 4 N2.1
Presentation of a group 19
Preserving an algebraic structure 38
Preserving group products 14 22
Primed element of a magnetic group 402
Primed element of the Newton group 168 171
Primed translation 417
Priming a translation 417
Primitive unit cell of a crystal 292
Primitive unit cell of a point lattice N8.2
Product of elements of a group 10
Proper see also Strictly
Proper  -equivalence class of matrix groups 79
Proper  -class (= proper arithmetic class) of matrix groups 81
Proper affine class of 2-dimensional magnetic space groups T11.2
Proper affine class of 3-dimensional magnetic space groups T17.3
Proper affine class of groups of isometries 122 T4.2
Proper affine class of magnetic groups 405
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