Isomorphism of lattices of subgroups of the layer and rod groups with sublattices of subgroups of the space groups

摘要

Following a brief overview of current knowledge on lattices of subgroups of the space groups, it is shown that in the case of reducible space groups those lattices contain sublattices which are lattice isomorphic to the lattices of subgroups of layer and rod groups. Both sublattices involve the sublattice consisting of equitranslational subgroups.