Opechowski W. — Crystallographic and metacrystallographic groups :: Электронная библиотека попечительского совета мехмата МГУ

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Opechowski W. — Crystallographic and metacrystallographic groups

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Название: Crystallographic and metacrystallographic groups

Автор: Opechowski W.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 628

Добавлена в каталог: 19.06.2005

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Предметный указатель

Colour space group      364 374
Colour symmetry groups      360
Colour W-group      355 383
Colour-group family of a group of isometries      367
Colour-group reduced family of a group of isometries      370
Coloured point set = colour function      353 375
Coloured point set generated by a colour group from a point      367 376
Colours      353
Column matrix of dimension n (= $n\times 1$ matrix)      90
Commensurate modulated point lattice      539
Commutator of two elements of a group      21
Commutator subgroup      21
Complement of a subset      4
Completely reduced matrix representation      134
Completely reducible matrix group      132
Complex conjugate matrix groups      77
Complex vector space      88
Complex vector space underlying a unitary vector space      520
Component point set of a composite point set      189
Components of a vector relative to a basis      89
Composite crystal      290 292
Composite point set      189
Composite point set having some symmetry      192
Composite set      39
Composite spin arrangement      487
Compound groups      360
Configuration space      522
Congruence of column matrices (modZ)      257
Congruent bases of a Euclidean vector space      110 120
Congruent coordinate systems of a Euclidean point space      120
Congruent groups of isometries      T4.2
Congruent groups of rotations      125
Congruent point sets      190 N7.2
Conjugate elements of a group      26
Conjugate permutations      34
Conjugate subgroups      25 47
Constituents of a direct sum of matrices      132
Constituents of a reduced matrix group      134
Constituents of a reducible matrix representation      134
Constituents of an algebraic structure      9
Constitutive relations of a medium      395
Continuous crystalline medium      496
Continuous geometrical crystalline medium      496
Continuous physical crystalline medium      496
Coordinate space (n-dimensional)      90
Coordinate systems differing only in their location in space      120
Coordinate systems in an affine point space      93 94
Coordinates of a point      93
Corepresentation (= matrix corepresentation) of a group by a group of complex matrices      78 526
Corepresentation (= matrix corepresentation) of a group by a group of unitary matrices      529
Corepresentation (= matrix corepresentation) of a group induced by a group of linear and antilinear transformations      525
Corepresentation (= matrix corepresentation) of a group induced by a group of unitary and antiumtary transformations      528 529
Corepresentation (= matrix corepresentation) of a group the unitary-antiunitary group      528
Corepresentation (= matrix representation) of the semilinear group      519 520 524
Corepresentation (one-dimensional) of the dihedral group of order 8      527
Corepresentation (one-dimensional) of the time group      529
Corepresentations of magnetic groups      520 532 N21.1
Coset Criterion      20
Cosets (left and right) of a subgroup      19
Cosets of a normal subgroup      20
Countable (= denumerable) set      5
Counterchange point symmetry      N12.4
Covariance of the Maxwell equations under a group      396
Covariance of the Maxwell equations under the discrete space-time group      394
Covariance of the Maxwell equations under the Newton group      396
Covariance of the Maxwell equations under the orientation-preserving Newton group      396
CR = constitutive relations of a medium      395 397
Criterion for the equivalence of permutation representations      72
Cryptosymmetries      360 N13.3
Crystal families = NWB systems of space groups      279
Crystal generated by a space group from a point = simple crystal      290
Crystal lattice      197
Crystal system (= ITC-system) of space groups      276
Crystal, composite      290
Crystal, geometrical      196 293 349
Crystal, ideal (= perfect)      293
Crystal, modulated      548
Crystal, physical      293 349 381
Crystal, real      293
Crystal, simple      290
Crystallographic colour group      364
Crystallographic colour group of rotations      370
Crystallographic d-colour group      360 364
Crystallographic equivalence (= proper affine equivalence) of crystallographic groups      264
Crystallographic equivalence of colour groups      370
Crystallographic group      11 187 196
Crystallographic group of rotations of a plane      164
Crystallographic group of rotations of space      21 123 157
Crystallographic group of rotations of space-time      = Heesch group
Crystallographic line group in space      326 T11.5
Crystallographic magnetic group      401
Crystallographic magnetic group of rotations in a plane      T15.4
Crystallographic magnetic group of rotations of space      T15.3
Crystallographic matrix group      262
Crystallographic orbit of a point under action of a space group      N10.2
Crystallographic spin group      505 515
Crystallographic subgroup of the space-time rotation group = Heesch group      169
Cubic Bravais system of point lattices      243 T8.3
Cubic geometric-class system of groups of rotations      T6.2 T6.5
Cubic group (= octahedral group) of proper rotations      155 T6.2 T6.5
Cubic ITC-system of space groups      T9.2.2
Cubic point lattice, body-centred      238 244
Cubic point lattice, face-centred      238 244
Cubic point lattice, primitive (= simple)      238 244
Curie's Principle      498
Cyclic group      17 47
Cyclic group of order 4      11
Cyclic group of rotations      154
Cyclic helical group      333
Decomposable discrete group of isometries      187 196 306 335
Decomposable matrix group      132 317
Decomposable representation of a group      135
Decomposition of a group into the cosets of a normal subgroup      20
Decomposition of a group into the left cosets of a subgroup      19
Decomposition of a group into the right cosets of a subgroup      20
Degree of a permutation      33
Denning relations of a group      19
Denumerable (= countable) set      5
Diagonalizable matrix      77
Dichromatic group = black-and-white group      354 374
Difference of two sets      4
Dihedral group of proper rotations      18 154
Dihedral matrix group of order 2n      18 75
Dihedral matrix group of order 6      18 26
Dihedral matrix group of order 8      27 T2.2 T2.3
Dimension of a corepresentation      524
Dimension of a Euclidean point space      95
Dimension of a representation      131
Dimension of a vector space      89
Dimension of an affine point space      92
Direct isometry      121 148 162
Direct product group      27
Direct product of carrier spaces of representations of a group      143
Direct product of matrices      143
Direct product of matrix representations      145
Direct product of two groups      52 53
Direct sum of matrices      132 134
Dirichlet domain = Dirichlet polyhedron      N8.8
Discrete group of isometries      187 189 N7.1
Discrete group of translations      195 205
Discrete helix      336
Discrete point set      187 188
Disjoint sets      3
Displacively modulated incommensurate crystal      537
Displacively modulated incommensurate point lattice      537
Distance between two points      99
Dodecahedral group = icosahedral group      156
Domain of influence      N8.8
Doppelgruppe — double group      N2.8a
Double group of a proper group of rotations      N2.8a

Double two-colour group      385
Eigenvalues of a matrix = characteristic values      76
Electric charge density      394
Electric current density      394
Electric dipole arrangement      356
electric dipole moment      349
Electric displacement      394
Electric field strength      394
Electric group      356 409
Electric quadrupole arrangements      N15.4
Electrically induced magnetoelectric effect      N19.3
Electrically ordered crystal      356
Electromagnetic quantities      349
Electromagnetic symmetry group of a medium = EMSG      397 497
Element left fixed by a permutation of a set      37
Element-wise invariance of a subset      37
Elements (of the Newton group) of the same kind      168
Elements of a set      3
Embedding a line in space      161
Embedding a plane in space      161 162
Empty set      3
EMSG      = electromagnetic symmetry group of a medium
Enantiomorphic Bravais classes of point lattices      221
Enantiomorphic Bravais groups      221
Enantiomorphic cyclic helical groups      336
Enantiomorphic groups of isometries      123
Enantiomorphic line groups      321
Enantiomorphic point sets      190
Enantiomorphic proper affine classes of line groups      322
Enantiomorphic proper arithmetic classes of Bravais groups      221
Enantiomorphic space groups      268
Enantiomorphism      268
Endomorphism      23
Energy eigenvalue      522
Epimorphism      23
Equality modulo an equivalence relation      7
Equality of ordered pairs      4
Equality of sets      3
Equivalence class = class      7 8
Equivalence relation on a set      6 8
Equivalent colour groups (equivalence classes: (Dl), (D2), (D3), (D4))      369
Equivalent corepresentations of a group      525
Equivalent d-colour functions = -colour point sets      378
Equivalent elements of a set      8
Equivalent elements of a subset relative to a group of permutations      39
Equivalent general positions      281
Equivalent groups of isometries      122 T4.2
Equivalent line groups      320 and 331
Equivalent magnetic groups      404
Equivalent matrices      76
Equivalent matrix groups      76 79
Equivalent matrix representations of a group      135
Equivalent metric forms      207
Equivalent net groups      310
Equivalent non-trivial spin groups      514
Equivalent permutation representations      71
Equivalent positions      281 304
Equivalent quadratic forms      207
Equivalent spin groups      514
Equivalent subgroups of the space-time group of rotations      169
Equivalent subsets of a set      39
Equivalent, weakly, irreducible representations of a group      Npr
Euclidean coordinate space      97
Euclidean group (= isometry group) of a Euclidean point space      38 103 115
Euclidean normalizer of a space group = Cheshire group      283 N9.9
Euclidean point space      8 98
Euclidean transformation      115
Euclidean vector space      95
Euler's function      47
Euler's theorem      150
Even permutation      34
Exceptional Bravais subclass of space groups      270
Exceptional space group      269
Extended modulated point lattice      541 546
Extended modulation function      541 546
Extended point lattice      541 546
Extension of a group by a group      52
Extension of a lattice group      N9.4
External semidirect product of groups      55 56
Extraordinary crystallographic orbit for a space group      N10.4
Factor group = quotient group      21
Faithful matrix representation of a group      24
Family of a group      61
Family of a group of proper rotations      157 T6.4
Ferrimagnetic helical spin arrangement      489
Ferrimagnetic spin arrangement      483
Ferroelectric crystalline medium      397 499
Ferroelectric dipole arrangement      494
Ferroelectric point group      494 T15.3 T19.1
Ferroelectric space group      398 494 N18.7
Ferromagnetic crystalline medium      397 499
Ferromagnetic point group      485 T15.3 T19.1
Ferromagnetic solid      490
Ferromagnetic space group      398 483 N18.7
Ferromagnetic spin arrangement = - spin lattice      420 483
Ferromagneto-electric crystalline medium      498
Ferromagneto-electric point group      494 T19.1
Ferromagneto-electric space group      494
Field      N2.1
Field of complex numbers      51
Field of real numbers      52
Finite group      11
Fixed-point-free group of isometries      153 252
Four-dimensional groups of the three-dimensional space      357
Four-group = Vierergruppe      11
Frobenius' congruences      257 274 276
Frobenius' Theorem      254 N9.2
Function belonging to a representation of the Newton group      388
Function constant in space      388
Function constant in time      388
Function defined on a set and having values in another set      41
Function from a set into a set      41
Function space      42
Function, value of a      41
Fundamental domain for a group of isometries      N7.1
Fundamental domain for a lattice group      292
Fundamental domain for a space group      292
Galois field      N2.1
General element of a set      39
General inhomogeneous linear group       113
General linear complex matrix group $GL(n, \mathbb C)$       16 76
General linear integral matrix group $GL(n, \mathbb Z)$       79
General linear rational matrix group $GL(n, \mathbb Q)$       79
General linear real matrix group $GL(n, \mathbb R)$       16 78
General position of a point      194 304
Generalized symmetry groups      360
Generating group of a point set      189
Generating group of a set      38
Generators of a subgroup      17
Geometric approach to the theory of space groups      198
Geometric class (= affine class) of crystallographic groups of rotations of a plane      163 T6.7
Geometric class (= affine class) of crystallographic groups of rotations of space      157 262 T6.2 T6.5
Geometric class (= affine class) of crystallographic groups of rotations of space-time = - Heesch groups      173 174 T6.8 T6.9 T6.10
Geometric class (= affine class) of crystallographic matrix groups      262
Geometric class (= affine class) of magnetic groups of rotations = - magnetic point groups      405
Geometric class (= affine class) of space groups      263 264
Geometric-class system of crystallographic groups of rotations      262 277
Geometrical crystal      196 197 293
Geometrical invariant of a cyclic group of rotations      191
Geometrical invariant of a glide reflection      153
Geometrical invariant of a proper rotation      153 191
Geometrical invariant of a reflection      153
Geometrical invariant of a screw displacement      153
Geometrical invariant of an inversion      153
Geometrical invariant of an isometry      153 154 N7.3
Geometrical invariants of a group of isometries      153 191
Glide line      163
Glide plane      152
Glide reflection in a line      163 259
Glide reflection in a plane      152 259

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