THE CONSTRUCTION OF UNITS OF INFINITE ORDER IN THE CHARACTER RING OF A FINITE GROUP

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The structure of the unit group consisting of units of finite order in the character ring of a finite group is well known (see [8]). We also have studied the unit group in the character ring of an alternating group ＄A_{n}(n￥geq 5)＄ . In this article our objective is to construct units of infinite order in the character ring of a finite group concretely, by making use of units in ＄Z[￥omega]＄ where ＄Z＄ is the ring of rational integers, ＄￥omega＄ is a primitive ＄p＄-th root of unity, and ＄p(￥geq 5)＄ is a prime number.

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