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On the Conjugacy Classes in an Integral Group Ring

Published online by Cambridge University Press:  20 November 2018

Alan Williamson
Alan Williamson*
Affiliation:
Pure Maths. Department, University College, P.O. Box 78 Cardiff, U.K.
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Let G be a periodic group and ZG its integral group ring. The elements ±g(g∈G) are called the trivial units of ZG. In [1], S. D. Berman has shown that if G is finite, then every unit of finite order is trivial if and only if G is abelian or the direct product of a quaternion group of order 8 and an elementary abelin 2-group. By comparison, Losey in [7] has shown that if ZG contains one non-trivial unit of finite order, then it contains infinitely many.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 491 - 496
Copyright
Copyright © Canadian Mathematical Society 1978

References

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