Abstract
Let G be a finite group and R(G) be the character ring of G. We determine the structure of the unit group U(R(G)) of R(G). Since R(G) is commutative, the torsion subgroup and the rank of U(R(G)) need to be determined. A theorem of Saksonov states that the torsion subgroup of U(R(G)) consists of the linear characters of G and their additive inverses. In this article, we give an explicit formula for the rank of U(R(G)).
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ACKNOWLEDGMENTS
The author thanks B. Külshammer for some valuable hints. This article is based on a part of the author's Ph.D. dissertation [Citation7].
Notes
Communicated by A. Turull.