Geodesic
Group Rings with Only Trivial Units of Finite Order
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1137-1138

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

We denote by ZG the integral group ring of the finite group G. S.D. Berman [1] showed that every unit of finite order μ in G is trivial (i.e., μ = ±g for some g in G) if and only if either G is abelian or G is a Hamiltonian 2-group. In this note, we give a new and shorter proof for the “only if” part. 
Hughes, Ian; Wei, Chou-Hsiang. Group Rings with Only Trivial Units of Finite Order. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1137-1138. doi: 10.4153/CJM-1972-120-1
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[1] 1. Berman, S. D., On the equation Xm = 1 in an integral group ring, Ukrain. Mat. Z. 7 (1955), 253–261. Google Scholar

[2] 2. Sehgal, S. K., On the isomorphism of integral group rings. I, Can. J. Math. 21 (1969), 410–413. Google Scholar

[3] 3. Sehgal, S. K., On the isomorphism of integral group rings. II, Can. J. Math. 21 (1969), 1182–1188. Google Scholar

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