An algebraic method for calculating crystallographic groups. II (Q2760688)

The first part of the article was published in [Sib. Zh. Ind. Mat. 3, No. 2(6), 43-62 (2000; Zbl 0969.20025)]. In the two parts of the article, a self-contained algebraic method is presented for calculating crystallographic groups acting in Euclidean and pseudo-Euclidean spaces. The general approach is illustrated by a classification of the groups acting in Euclidean 3-space, which was first given by geometric methods in works of E.~S.~Fedorov and A.~Schoenflies in the XIX-th century.NEWLINENEWLINENEWLINEThe second (final) part contains a classification of the Euclidean crystallographic groups by the methods developed in the first part with detailed calculations. In the last two sections, some connections with physics are presented. The generalized Bragg interference condition for X-rays in crystals and a wave interpretation of the X-ray analysis of crystal structures are considered.