AN ARITHMETICAL CHARACTERIZATION OF FINITE ELEMENTARY 2-GROUPS

Beginning with Carlitz's well known characterization of algebraic number rings with class number two, arithmetical characterizations of divisor class groups have been a topic of interest in the literature. In this note we develop a characterization of Dedekind domains with finite elementary 2-group class group. The characterization is in terms of the asymptotic behavior of the number of distinct factorizations of powers of an irreducible element.