Geodesic
Units in group rings of crystallographic groups
Karel Dekimpe1
1 Katholieke Universiteit Leuven Campus Kortrijk B-8500 Kortrijk, Belgium
Fundamenta Mathematicae, Tome 179 (2003) no. 2, pp. 169-178

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In \cite{ms98-1}, 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.
DOI : 10.4064/fm179-2-4
Keywords: cite authors initiated technique using affine representations study groups units integral group rings crystallographic groups paper approach special classes crystallographic groups first class groups obtain normal complement group inside group normalized units second class groups zassenhaus conjectures valid generalizes results known infinite dihedral group

Karel Dekimpe 1

1 Katholieke Universiteit Leuven Campus Kortrijk B-8500 Kortrijk, Belgium 
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Karel Dekimpe. Units in group rings of crystallographic groups. Fundamenta Mathematicae, Tome 179 (2003) no. 2, pp. 169-178. doi: 10.4064/fm179-2-4

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