International Tables for Crystallography (2011). Vol. A1, ch. 1.4, pp. 27-40   | 1 | 2 |
https://doi.org/10.1107/97809553602060000793

Chapter 1.4. The mathematical background of the subgroup tables

Chapter index

Abelian group 1.4.3.1
action of a group on a set 1.4.3.2
affine group 1.4.2.4, 1.4.2.4
affine mapping 1.4.2.4
affine normalizers 1.4.8
affine space 1.4.2.3
alternating group 1.4.3.6
associative law 1.4.3.1
automorphism 1.4.3.4
automorphism group 1.4.2.2
basis 1.4.2.2
basis of a vector space 1.4.2.2
CARAT (computer package) 1.4.2.1
centralizer 1.4.3.2
characteristic subgroup 1.4.3.5
coefficients of a vector 1.4.2.2
complement 1.4.4.2
composition, law of 1.4.3.1
congruence 1.4.5.1
trivial 1.4.5.1
conjugation action 1.4.3.2
core of a subgroup 1.4.3.2
cosets, left and right 1.4.3.2, 1.4.3.2
crystal space 1.4.2.1
crystal structure 1.4.4.1
cyclic group 1.4.3.1
derived series 1.4.5.2
derived subgroup 1.4.5.2
dimension of a vector space 1.4.2.2
direct product of two groups 1.4.3.6
direct space 1.4.2.1
distance 1.4.2.4
elementary Abelian p-group 1.4.4.2
Euclidean group 1.4.2.4
Euclidean metric 1.4.2.4
Euclidean point space 1.4.2.4
Euclidean vector space 1.4.2.2
factor group 1.4.3.2
faithful action 1.4.3.2
faithful -set 1.4.3.2
finite field 1.4.3.2
Galois, theorem of 1.4.5.1
generators 1.4.3.1
groups 1.4.3.1
Abelian 1.4.3.1
alternating 1.4.3.6
automorphism 1.4.2.2
cyclic 1.4.3.1
Euclidean 1.4.2.4
factor 1.4.3.2
isomorphic 1.4.3.4, 1.4.3.4
linear 1.4.2.2
orthogonal 1.4.2.2
site-symmetry 1.4.3.2
soluble 1.4.5.2, 1.4.5.3
symmetric 1.4.3.6
Hermann, theorem of 1.4.4.2, 1.4.8
homomorphism 1.4.3.4
injective 1.4.3.4
kernel of 1.4.3.4
identity mapping (operation) 1.4.3.1
index of a subgroup 1.4.3.2, 1.4.5.3, 1.4.6, 1.4.7.2, 1.4.7.2
injective homomorphism 1.4.3.4
inverse operation 1.4.3.1
isometry 1.4.2.4
isomorphic groups 1.4.3.4, 1.4.3.4
isomorphic -sets 1.4.3.4
isomorphic space groups 1.4.7.1
isomorphism 1.4.3.4
isomorphism theorems 1.4.3.5
kernel
of a homomorphism 1.4.3.4
of the action 1.4.3.2, 1.4.3.2
klassengleiche (k-) subgroups 1.4.4.2, 1.4.4.2
klassengleiche (k-) supergroups 1.4.8
Lagrange, theorem of 1.4.3.2
lattice 1.4.4.1
law of composition 1.4.3.1
left coset 1.4.3.2
linear group 1.4.2.2
linear mapping 1.4.2.2
linear part 1.4.2.4
mapping
affine 1.4.2.4
identity 1.4.3.1
linear 1.4.2.2
maximal subgroups 1.4.4.2, 1.4.5
of soluble groups 1.4.5.3
minimal supergroups 1.4.8
normalizers 1.4.3.2
affine 1.4.8
normal subgroups 1.4.3.2
orbit 1.4.3.2
order of a group 1.4.3.1, 1.4.6.2
orthogonal group 1.4.2.2
point space 1.4.2.1, 1.4.2.3
primitive -set 1.4.5.1
product of group elements 1.4.3.1
right coset 1.4.3.2
-sets 1.4.3.2
faithful 1.4.3.2
isomorphic 1.4.3.4
primitive 1.4.5.1
transitive 1.4.3.2
site-symmetry group 1.4.3.2
soluble group 1.4.5.2, 1.4.5.3
space groups 1.4.4.1, 1.4.6.2
isomorphic 1.4.7.1
subgroups of 1.4.4.2
symmorphic 1.4.4.2
stabilizer 1.4.3.2, 1.4.4.1
subgroups 1.4.3.1
characteristic 1.4.3.5
derived 1.4.5.2
index of 1.4.7.2, 1.4.7.2
klassengleiche 1.4.4.2
maximal 1.4.4.2, 1.4.5
normal 1.4.3.2
of space groups 1.4.4.2
translation 1.4.2.4, 1.4.4.1
translationengleiche 1.4.4.2
trivial 1.4.3.1
supergroups 1.4.8
klassengleiche 1.4.8
minimal 1.4.8
translationengleiche 1.4.8
Sylow, theorems of 1.4.3.3
Sylow p-subgroup 1.4.3.3
symmetric group 1.4.3.6
symmorphic space groups 1.4.4.2
theorems
Galois's theorem 1.4.5.1
Hermann's theorem 1.4.4.2, 1.4.8
isomorphism theorems 1.4.3.5
Lagrange's theorem 1.4.3.2
Sylow's theorems 1.4.3.3
transitive -set 1.4.3.2
translation 1.4.2.4
translationengleiche (t-) subgroups 1.4.4.2
translationengleiche (t-) supergroups 1.4.8
translation subgroup 1.4.2.4, 1.4.4.1
trivial congruence 1.4.5.1
trivial subgroup 1.4.3.1
underlying vector space 1.4.2.3
unit element 1.4.3.1
vector 1.4.2.2
coefficients of 1.4.2.2
vector space 1.4.2.2
dimension of 1.4.2.2
Euclidean 1.4.2.2
underlying 1.4.2.3