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

Global symmetry group of a point set      194
Globally fixed geometrical invariant      153
Goursat's Rule for constructing subdirect products      317
Goursat's theorem      65
Greek element of a direct product group      60 436
Grey space group      361
Group      8 10
Group action = action of a group      44
Group of a J-vector      397
Group of a P-vector      397
Group of affine transformations referred to a coordinate system      117 122
Group of all affine transformations of an affine space = affine group      110
Group of all isometries of a Euclidean point space = Euclidean group      115
Group of all translations of an affine space      111
Group of an M-vector      397
Group of antisymmetry      358
Group of automorphisms of a complex vector space      523
Group of automorphisms of a group      45
Group of cambiant symmetry      360
Group of isometries      = subgroup of a Euclidean group
Group of linear and antilinear transformations      526
Group of linear transformations referred to a basis      107
Group of permutations      14
Group of permutations generated by a subgroup      68
Group of permutations of a set      32
Group of primitive translations      259
Group of proper and improper rotations      62 201
Group of rotations at a point      116 148 149 163
Group of rotations of a plane      162
Group of rotations of space = point group      149
Group of rotations of space-time = subgroup of the space-time rotation group      169
Group of rotations of the first kind      156
Group of rotations of the second kind with inversion      156
Group of rotations of the second kind without inversion      156
Group of symmetry and antisymmetry      361
Group of transformations of a set onto itself      32
Group of various kinds of antisymmetry      360
Group product      = product of elements of a group
H-M symbols      = Hermann — Mauguin symbols
h-subgroup      62
Handedness = orientation      119
Heesch group = crystallographic group of space-time rotations      174 361 394 573
Heesch group compatible with a crystalline medium      498
Heesch — Shubnikov group      356 361 N12.8
Helical group      153 195 332 Nll.l
Helical spin arrangement      489
Helix, irrational discrete      336
Helix, rational discrete      336
Hemisymmorphic space group      N9.3
Hermann — Mauguin symbols (= H-M symbols = international symbols), full and short      0
Hermann — Mauguin symbols for the Bravais subclasses of an affine class of space groups      273
Hermann — Mauguin symbols for the groups of rotations in a plane      163 164 T6.7
Hermann — Mauguin symbols for the line groups in a plane      312 Tll.1.1 Tll.1.2
Hermann — Mauguin symbols for the line groups of space      325
Hermann — Mauguin symbols for the magnetic groups of rotations (= magnetic point groups)      408
Hermann — Mauguin symbols for the net groups of space      312 T11.2
Hermann — Mauguin symbols for the one-dimensional space groups      274
Hermann — Mauguin symbols for the three-dimensional magnetic space groups M of the kind $\mathbf{M_R}$       450
Hermann — Mauguin symbols for the three-dimensional magnetic space groups M of the kind $\mathbf{M_T}$       442
Hermann — Mauguin symbols for the two- and three-dimensional space groups      279 280 281
Hermann — Mauguin symbols for the two-dimensional magnetic space groups      224
Hermann — Mauguin symbols, modified, for the groups of rotations of space      158 T6.5
Hermann — Mauguin symbols, modified, for the subgroups of the space-time rotation group      170 T6.8 T6.9
Hermann — Mauguin symbols, standard, for the groups of rotations of space      155 158 T6.5
Hermann — Mauguin symbols, standard, for the subgroups of the space-time rotation group      170 T6.8 T6.9
Hermann's Theorem      260
Hermitian adjoint of a matrix      77
Hermitian form associated with a basis of a unitary vector space      521
Hermitian inner product (= scalar product) of two vectors      520 521
Hermitian matrix      77
Hexagonal Bravais system of point lattices (two- and three-dimensional)      T8.2 T8.3
Hexagonal Bravais system of space groups (two- and three-dimensional)      T9.1.3 T9.2.3
Hexagonal geometric-class system of groups of rotations (of a plane and of space)      T6.2 T6.5 T6.7
Hexagonal groups of rotations (of a plane and of space)      T6.2 T6.5 T6.7
Hexagonal ITC-system of space groups (two- and three-dimensional)      T9.1.3 T9.2.2
Hexagonal point lattice (two- and three-dimensional)      234 243 244
Hilbert space      N21.2
Him G      50
Holohedral class of groups of rotations      216 T6.2
Holohedral group of rotations      216
Holohedral matrix group      217
Holohedry of a magnetic point lattice      422
Holohedry of a magnetic point lattice at one of its points      422
Holohedry of a point lattice      216
Holohedry of a point lattice at a point      215
Holomorph of a group      45 50
Homogeneity of a transitive set      39
Homomorphism of a group into a group      23
Homomorphism of a group onto a group      22
Homomorphism theorem      23
Homomorphisms with the same kernel      50
I-groups of space-time rotations      156 168 173 T6.8
Icosahedral group (= dodecahedral group) of proper rotations      21 156 408 Npr
Ideal crystal      293
Identification      358
Identity automorphism      45 52
Identity element (= unit element) of a group      10
Identity permutation      31
Identity permutation representation of a group      70
Identity representation of a group      24 135
Identity rotation      13
Image of a group      Npr
Image of a homomorphism      23
Image of an element of a set under a mapping      5
Image of an irreducible representation of a group      Npr
Imperfect crystal      355
Improper motion = opposite isometry      121
Improper rotation      116 121 148 150 162
Improper subgroup      15
Incommensurate crystal      197 537
Incommensurate modulated point lattice      539
Indecomposable constituents of a matrix group      134
Indecomposable discrete group of isometries = space group      187 196 N7.7
Indecomposable matrix group      132 133
Indecomposable representation of a group      135
Index 2 Lemma      29
Index of a subgroup      19
Index-2 subgroups of a lattice group      414 417 T16.1 T16.2
Inducing a linear transformation by an affine transformation      110
Inequivalent matrix groups      76
Inequivalent matrix representations      135
Infinite axial group of rotations      160 T6.6
Infinite group      11
Infinite index of a subgroup      19
Infinite subgroups of the affine group      T4.1
Infinite-dimensional (complex or real) vector space      89 N21.2
Inhomogeneous linear transformation      112 N4.2
Inhomogeneous Lorentz group = Poincare group      N6.5
Inhomogeneous orthogonal-matrix group      116
Inhomogeneous rotation-matrix group associated with a basis      116
Injection      5
Inn G      46
Inner automorphism      46
Inner product (= scalar product) of two vectors      95 519
Inner product of two rays      521
Instant      87 101 165
Integral linear combination of lattice vectors      202
Integral matrix      79
Integral matrix group      = subgroup of $GL(n</a></span> <span class=subjpages><a href=

$GL(n</a></span> <span class=subjpages><a href=

\mathbb
Internal semidirect product of groups      56
International symbols = Hermann — Mauguin symbols      158
Intersection of two groups      16
intersection of two sets      3
Intransitive group of permutations      39
Intransitive set      39
Invariance group of a function      44
Invariance group of a magnetic dipole arrangement      = - a spin arrangement
Invariance group of a physical crystal      381
Invariance group of a point set      191
Invariance group of a spin arrangement      400

Invariance group of a subset      37 38
Invariance group of an atomic system      529 530
Invariance group of an electric dipole arrangement      408
Invariance group of the constitutive relations      397
Invariance of a point set under an isometry      191
Invariance of a subset under a permutation      37
Invariant spin arrangement      N18.2
Invariant spin of a magnetic site group      478
Invariant spin of a magnetically admissible group of rotations      T18.1
Invariant subgroup = normal subgroup      47
Invariant subspace of a carrier space      138
Invariant vector of a group in a carrier space      138
Inverse of a permutation      31
Inverse of an element of a group      10
Inversion = space inversion      150 152 167
Inversion group      151
Inversion group of a line      165
Inversion point      151
Irrational angle      161
Irrational discrete helix      336
Irrational helical spin arrangement      489 N18.5
Irrational lattice group      550
Irrational point lattice      550
Irrational standard basis      550
Irreducible carrier space      138
Irreducible constituents of a matrix group      134
Irreducible matrix group      132 135
Irreducible representation of a group      135
Irreducible representations of the dihedral group      T5.1
Iso G      49
Isometric Euclidean point spaces      127
Isometric Euclidean vector spaces      127
Isometry group = Euclidean group      103
Isometry of a Euclidean point space      115 116
Isomorph of a group      45 47
Isomorphism class of crystallographic groups of rotations of space      T6.3
Isomorphism class of groups      8 14
Isomorphism class of groups of isometries      123
Isomorphism class of space groups      123 262
Isomorphism of affine spaces      93
Isomorphism of groups      14
Isomorphism of vector spaces      90
IT-number of a space group      272
ITC      = either ITC 52 or ITC 83
ITC 52 = International Tables for X-Ray Crystallography, Vol. I      158 197
ITC 83 = International Tables for Crystallography, Vol. A      158 197
ITC-system of affine classes of space groups      277
ITC-system of arithmetic classes of space groups      277
ITC-system of geometric classes of space groups      277
J-Heesch group      397 T19.1
J-Heesch — Shubnikov group      494
Jacobi matrix      100 125 T3.1
Jacobi transformation      100 N3.4
JM-Heesch group      397 T19.1
Jordan's Theorem      222 268 N8.5
JP-Heesch group      397 T19.1
Junior group of symmetry and antisymmetry      361
K-class of simple point sets      294
K-orbit of a point      189
Kernel of a homomorphism      23
Klassengleiche Untergruppe = R-subgroup      261
Kramers operator      531 N21.6
Kronecker product (= direct product) of matrices      143
Kronecker product (= direct product) of matrix representations      143 145
Kronecker symbol      36
Lagrange's theorem      19
Latin element of a direct product group      60 436
Lattice      = point lattice
Lattice group      187 195 201
Lattice line      201
Lattice of a Bravais superspace group      552
Lattice of a magnetic space group      439
Lattice of a space group      250
Lattice of an infinite decomposable group of isometries      306
Lattice plane      201
Lattice point      201
Lattice vector      201
Layer group      = net group
Leader of a Bravais flock      227 240 269
Left cosets of a subgroup      8 19
Left-coset array for a site group of a space group      291 T10.1.1
Left-handed coordinate systems      120
Length of a translation      116
Line = one-dimensional Euclidean point space      164
Line group      196 306 N7.4 Nll.l
Line group as a subgroup of a two-dimensional space group      313
Line group associated with a pair of quotient groups      320 T11.4
Line group associated with a two-dimensional group of rotations and a one-dimensional space group      316
Line group in a plane      311 Tll.l
Line group in space      311 T11.5
Line in an affine space      93
Linear combination of vectors      89
Linear component of a rigid motion      N4.4
Linear constituent of a rigid motion      N4.4
Linear group of a vector space      103 104
Linear independence of vectors      89
Linear part of an affine transformation      113 128
Linear part of an element of a magnetic space group      439
Linear part of an element of the Newton group      166 438
Linear part of an isometry      116 128 N4.4
Linear transformation of a vector space      104 113
Linearly independent translations      115
Local symmetry group of a point set      194
Local symmetry of a point set      194
Lorentz equations      398
Lorentz group (inhomogeneous) = Perineal group      N6.5
M-Heesch group      397 T15.3 T19.1
M-Heesch-Shubnikov group      494
Macromolecule      196 328
Macroscopic field equations of Maxwell      394 398
Magnetic basis of a magnetic lattice group      418 T16.2
Magnetic basis of a magnetic point lattice      422 T16.2
Magnetic Bravais class      423
Magnetic charge density      396 N16.3
Magnetic coordinate system for a magnetic lattice group      418
Magnetic coordinate system for a magnetic point lattice      422
Magnetic crystal      475
Magnetic dipole arrangement (— spin arrangement)      355
Magnetic dipole moment      349
Magnetic families of the groups      422
Magnetic families of the groups; 4mm; 42m      T15.1
Magnetic family of a group of isometries      404
Magnetic family of a lattice group      417
Magnetic family of the group 4/mmm      T15.2
Magnetic field strength      394
Magnetic group      62 356 357 375
Magnetic group (Definition (D2))      402 N15.2
Magnetic group (Definition (Dl))      401 N15.2
Magnetic group corresponding to a two-colour group      375 406
Magnetic group of rotations = magnetic point group      401 406
Magnetic induction      394
Magnetic lattice group      401 406
Magnetic lattice group coholohedral with a lattice group      422
Magnetic line group      401
Magnetic linear group $ML(n, \mathbb Z)$       419 N16.2
Magnetic net group      401
Magnetic order      490
Magnetic point group = magnetic group of rotations      401 406
Magnetic point lattice      420
Magnetic point lattice generated by a magnetic lattice group      420
Magnetic site group      477
Magnetic site point group      477
Magnetic space group      359 401
Magnetic space group, one-dimensional      437 T11.1.1
Magnetic space group; 2-dimensional      437 T11.2
Magnetic space group; 2-dimensional, corresponding to a net group      436
Magnetic space group; 2-dimensional, corresponding to a two-colour space group      436
Magnetic space group; 3-dimensional, corresponding to a two-colour three-dimensional space group      437
Magnetic space group; 3-dimensional, of the kind $\mathbf{M_R}$       436 438
Magnetic space group; 3-dimensional, of the kind $\mathbf{M_T}$       436 438

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