In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the infinite dihedral group.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-4,
author = {Karel Dekimpe},
title = {Units in group rings of crystallographic groups},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {169-178},
zbl = {1085.16023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-4}
}
Karel Dekimpe. Units in group rings of crystallographic groups. Fundamenta Mathematicae, Tome 177 (2003) pp. 169-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-4/