Geodesic
The Group of Units of the Integral Group Ring ZS3
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 529-534

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We denote by ZG the integral group ring of the finite group G. We call ±g, for g in G, a trivial unit of ZG. For G abelian, Higman [4] (see also [3, p. 262 ff]) showed that every unit of finite order in ZG is trivial. For arbitrary finite G (indeed, for a torsion group G, not necessarily finite), Higman [4] showed that every unit in ZG is trivial if and only if G is (i) abelian and the order of each element divides 4, or (ii) abelian and the order of each element divides 6, or (iii) the direct product of the quaternion group of order 8 and an abelian group of exponent 2. 
Hughes, I.; Pearson, K. R. The Group of Units of the Integral Group Ring ZS3. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 529-534. doi: 10.4153/CMB-1972-093-1
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     title = {The {Group} of {Units} of the {Integral} {Group} {Ring} {ZS3}},
     journal = {Canadian mathematical bulletin},
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     year = {1972},
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     doi = {10.4153/CMB-1972-093-1},
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