On groups occurring in the theory of crystal multi-lattices (Q1806020)

Generalized lattice groups, also referred to as lattice groups for multi-lattices have been introduced to study some problems in crystallography. The structure of these groups is not completely known, and it is the purpose of the paper to contribute a better understanding of this question. After some preliminaries on the description of multi-lattices, the group is defined, and some properties are stated. Then one characterizes all the elements of the group of which the \(m\)-th powers are the unit transformation. Then the various configurations are classified and some illustrative lattice examples are given.