Geodesic
Trivial Units in Group Rings
Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 60-62

Voir la notice de l'article provenant de la source Cambridge University Press

Let $G$ be an arbitrary group and let $U$ be a subgroup of the normalized units in $\mathbb{Z}G$ . We show that if $U$ contains $G$ as a subgroup of finite index, then $U\,=\,G$ . This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.
DOI : 10.4153/CMB-2000-008-0
Mots-clés : 16S34, 16U60, units, trace, finite conjugate subgroup 
Farkas, Daniel R.; Linnell, Peter A. Trivial Units in Group Rings. Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 60-62. doi: 10.4153/CMB-2000-008-0
@article{10_4153_CMB_2000_008_0,
     author = {Farkas, Daniel R. and Linnell, Peter A.},
     title = {Trivial {Units} in {Group} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {60--62},
     year = {2000},
     volume = {43},
     number = {1},
     doi = {10.4153/CMB-2000-008-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-008-0/}
}
TY  - JOUR
AU  - Farkas, Daniel R.
AU  - Linnell, Peter A.
TI  - Trivial Units in Group Rings
JO  - Canadian mathematical bulletin
PY  - 2000
SP  - 60
EP  - 62
VL  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-008-0/
DO  - 10.4153/CMB-2000-008-0
ID  - 10_4153_CMB_2000_008_0
ER  - 
%0 Journal Article
%A Farkas, Daniel R.
%A Linnell, Peter A.
%T Trivial Units in Group Rings
%J Canadian mathematical bulletin
%D 2000
%P 60-62
%V 43
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-008-0/
%R 10.4153/CMB-2000-008-0
%F 10_4153_CMB_2000_008_0

[1] [1] Marciniak, Z. S. and Sehgal, S. K., Units in group rings and geometry.Methods in Ring Theory, Levico Terme, Italy, (eds., V. S. Drensky, A. Giambruno, and S. K. Sehgal), Lecture Notes in Pure and Applied Math. 198, Marcel Dekker, New York, 1998, 185–198. Google Scholar

[2] [2] Sehgal, S. K., Topics in group rings. Pure and Applied Math. 50, Marcel Dekker, New York, 1978. Google Scholar

[3] [3] Sehgal, S. K., Units in integral group rings. Pitman Monographs and Surveys in Pure and Applied Math. 69, Longman Scientific, Harlow, 1993. Google Scholar

Cité par Sources :