Crystallographic classes in a 4-dimensional Minkowski space

On a crystallographic group, a condition of being topologically discrete is imposed which is weaker than is the conventional requirement for an action on space to be discontinuous. Isomorphism classification is given for crystallographic groups in three crystallographic classes in a 4-dimensional Minkowski space, which are defined by unimodular subgroups of the general Lorentz group. In these classes are, respectively, 24, 36, and 68 crystallographic groups. __________ Translated from Algebra i Logika, Vol. 47, No. 1, pp. 31–53, January–February, 2008.