Results for by Wondratschek, H.
Conjugate elements and conjugate subgroups
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.4.3, p.
numbers of subgroups, i.e. have different lengths. Equation (1.2.4.1) can be written Using conjugation, Definition 1.2.4.2.3 can be formulated as Definition 1.2.4.3.3.  A subgroup of a group ...

Definition
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.4.1, p.
introduction to the subgroups of space groups There may be sets of elements that do not constitute the full group but nevertheless fulfil the group postulates for themselves. Definition 1.2.4.1.1.  A subset of elements ...

Subgroups
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.4, p.
of into the same cosets: Subgroups that fulfil equation (1.2.4.1) are called `normal subgroups' according to the following definition: Definition 1.2.4.2.3.  A subgroup is called a normal sub­group or invariant subgroup ...

Coset decomposition and normal subgroups
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.4.2, p.
subgroups' according to the following definition: Definition 1.2.4.2.3.  A subgroup is called a normal sub­group or invariant subgroup of,, if equation (1.2.4.1) is fulfilled. The relation always ...

Factor groups and homomorphism
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.4.4, p.
introduction to the subgroups of space groups For the following definition, the `product of sets of group elements' will be used: Definition 1.2.4.4.1.  Let be a group and, be two arbitrary sets of its elements which ...

Normalizers
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.4.5, p.
Definition 1.2.4.5.1.  The set of all elements that map the subgroup onto itself by conjugation,, forms a group, called the normalizer of in, where . Remarks (1) The group is a normal ...