An algebraic method for calculating crystallographic groups. I (Q2713989)

The article opens a series of papers on a self-contained algebraic method for calculating crystallographic groups acting in Euclidean and pseudo-Euclidean spaces. The general approach proposed is illustrated by the classification of groups acting in Euclidean 3-space, which first was given by geometric methods in works of E.~S.~Fedorov and A.~Schönflies in the XIX-th century.NEWLINENEWLINENEWLINEThe article actually does not contain any new mathematical ideas but a clear algebraic view of the crystallographic groups that could be useful for various specialists interested in modern crystallography.