Lemmata on subgroups of space groups
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.8,
p.
[ doi:10.1107/97809553602060000791 ]
dimensional space groups. They are valid by analogy for the (two-dimensional) plane groups.
1.2.8.1. General lemmata
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Lemma
1.2.8.1.1. A subgroup of a space group is a space group again, if and only ...
Lemmata on maximal subgroups
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.8.2,
p.
[ doi:10.1107/97809553602060000791 ]
introduction to the subgroups of space groups
Even the set of all maximal subgroups of finite index is not finite, as can be seen from the following lemma.
Lemma
1.2.8.2.1. The index i of a maximal subgroup ...
General lemmata
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.8.1,
p.
[ doi:10.1107/97809553602060000791 ]
introduction to the subgroups of space groups
Lemma
1.2.8.1.1. A subgroup of a space group is a space group again, if and only if the index is finite.
In this volume, only subgroups of finite index i ...
