The Units of Character Fields and the Central Units of Integer Group Rings of Finite Groups

The article is devoted to studying the relations between the units of character fields and the central units of integer group rings. It is shown that some power of a unit of a character field always results in a central unit (Theorem 1). To determine this power, the exponent is found of the unit group of the quotient ring of the integer ring of an abelian field by a power of a prime ideal (Theorem 2), and this exponent is used to answer the question 12.1. b in the “Kourovka Notebook” (Theorem 3).