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

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DOI

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
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     author = {Farkas, Daniel R. and Linnell, Peter A.},
     title = {Trivial {Units} in {Group} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {60--62},
     year = {2000},
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     number = {1},
     doi = {10.4153/CMB-2000-008-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-008-0/}
}
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