Units in group rings of crystallographic groups
Fundamenta Mathematicae (2003)
- Volume: 179, Issue: 2, page 169-178
- ISSN: 0016-2736
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topKarel Dekimpe. "Units in group rings of crystallographic groups." Fundamenta Mathematicae 179.2 (2003): 169-178. <http://eudml.org/doc/283040>.
@article{KarelDekimpe2003,
abstract = {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.},
author = {Karel Dekimpe},
journal = {Fundamenta Mathematicae},
keywords = {affine representations; groups of units; integral group rings of crystallographic groups; normal complements; groups of normalized units; Zassenhaus conjectures},
language = {eng},
number = {2},
pages = {169-178},
title = {Units in group rings of crystallographic groups},
url = {http://eudml.org/doc/283040},
volume = {179},
year = {2003},
}
TY - JOUR
AU - Karel Dekimpe
TI - Units in group rings of crystallographic groups
JO - Fundamenta Mathematicae
PY - 2003
VL - 179
IS - 2
SP - 169
EP - 178
AB - 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.
LA - eng
KW - affine representations; groups of units; integral group rings of crystallographic groups; normal complements; groups of normalized units; Zassenhaus conjectures
UR - http://eudml.org/doc/283040
ER -
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