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).