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Group Rings with Only Trivial Units of Finite Order

Published online by Cambridge University Press:  20 November 2018

Ian Hughes  and
Chou-Hsiang Wei
Ian Hughes
Affiliation:
Queen's University, Kingston, Ontario
Chou-Hsiang Wei
Affiliation:
Queen's University, Kingston, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1137 - 1138
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Berman, S. D., On the equation Xm = 1 in an integral group ring, Ukrain. Mat. Z. 7 (1955), 253–261.Google Scholar
2. Sehgal, S. K., On the isomorphism of integral group rings. I, Can. J. Math. 21 (1969), 410–413.Google Scholar
3. Sehgal, S. K., On the isomorphism of integral group rings. II, Can. J. Math. 21 (1969), 1182–1188.Google Scholar