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International Tables for Crystallography (2006). Vol. A1. ch. 1.5, pp. 29-40
https://doi.org/10.1107/97809553602060000541 |
Chapter 1.5. The mathematical background of the subgroup tables
Chapter index
Abelian group 1.5.3.1
action of a group on a set 1.5.3.2
affine group 1.5.2.4
affine mapping 1.5.2.4
affine space 1.5.2.3
alternating group 1.5.3.6
automorphism 1.5.3.4
automorphism group 1.5.2.2
basis of a vector space 1.5.2.2
CARAT 1.5.2.1
centralizer 1.5.3.2
characteristic subgroup 1.5.3.5
coefficients of a vector 1.5.2.2
complement 1.5.4.2
composition, law of 1.5.3.1
conjugation action 1.5.3.2
core of a subgroup 1.5.3.2
crystal space 1.5.2.1
crystal structure 1.5.4.1
cyclic group 1.5.3.1
derived series 1.5.5.2
derived subgroup 1.5.5.2
dimension of a vector space 1.5.2.2
direct product of two groups 1.5.3.6
direct space 1.5.2.1
distance 1.5.2.4
elementary Abelian p-group 1.5.4.2
Euclidean affine space 1.5.2.4
Euclidean group 1.5.2.4
Euclidean metric 1.5.2.4
Euclidean vector space 1.5.2.2
factor group 1.5.3.2
faithful action 1.5.3.2
faithful -set 1.5.3.2
finite field 1.5.3.2
generators 1.5.3.1
groups 1.5.3.1
Abelian 1.5.3.1
affine 1.5.2.4
alternating 1.5.3.6
automorphism 1.5.2.2
cyclic 1.5.3.1
Euclidean 1.5.2.4
factor 1.5.3.2
isomorphic 1.5.3.4
linear 1.5.2.2
orthogonal 1.5.2.2
soluble 1.5.5.2
symmetric 1.5.3.6
Hermann, theorem of 1.5.4.2
index of a subgroup 1.5.3.2
injective homomorphism 1.5.3.4
inverse operation 1.5.3.1
isometry 1.5.2.4
isomorphic groups 1.5.3.4
isomorphic -sets 1.5.3.4
isomorphism 1.5.3.4
isomorphism theorems 1.5.3.5
Lagrange, theorem of 1.5.3.2
lattice 1.5.4.1
law of composition 1.5.3.1
left coset 1.5.3.2
linear group 1.5.2.2
linear mapping 1.5.2.2
linear part 1.5.2.4
normalizers 1.5.3.2
normal subgroups 1.5.3.2
orbit 1.5.3.2
order of a group 1.5.3.1
orthogonal group 1.5.2.2
point space 1.5.2.3
primitive -set 1.5.5.1
product of group elements 1.5.3.1
right coset 1.5.3.2
-set 1.5.3.2
soluble group 1.5.5.2
stabilizer 1.5.3.2
subgroups 1.5.3.1
characteristic 1.5.3.5
derived 1.5.5.2
klassengleiche 1.5.4.2
normal 1.5.3.2
translationengleiche 1.5.4.2
trivial 1.5.3.1
Sylow, theorems of 1.5.3.3
Sylow p-subgroup 1.5.3.3
symmetric group 1.5.3.6
symmorphic space groups 1.5.4.2
theorems
Hermann's theorem 1.5.4.2
isomorphism theorems 1.5.3.5
Lagrange's theorem 1.5.3.2
Sylow's theorems 1.5.3.3
transitive -set 1.5.3.2
translation 1.5.2.4
trivial congruence 1.5.5.1
trivial subgroup 1.5.3.1
underlying vector space 1.5.2.3
unit element 1.5.3.1