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.

Keywords:

units, trace, finite conjugate subgroup units, trace, finite conjugate subgroup

MSC Classifications:

16S34, 16U60 show english descriptions Group rings [See also 20C05, 20C07], Laurent polynomial rings
Units, groups of units 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings
16U60 - Units, groups of units

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